Works (179)

Updated: April 4th, 2024 04:14

2024 article

Perspective functions with nonlinear scaling

Briceno-Arias, L. M., Combettes, P. L., & Silva, F. J. (2024, February 19). COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, Vol. 2.

By: L. Briceno-Arias*, P. Combettes n & F. Silva*

author keywords: Convex analysis; Legendre conjugate; perspective function; nonlinear scaling
Sources: Web Of Science, NC State University Libraries
Added: March 18, 2024

2024 journal article

The geometry of monotone operator splitting methods (to appear, available on arxiv)

Acta Numerica.

Contributors: P. Combettes

Source: ORCID
Added: November 3, 2023

2023 article

A Perturbation Framework for Convex Minimization and Monotone Inclusion Problems with Nonlinear Compositions

Briceno-Arias, L. M., & Combettes, P. L. (2023, October 17). MATHEMATICS OF OPERATIONS RESEARCH, Vol. 10.

By: L. Briceno-Arias* & P. Combettes n

author keywords: convex optimization; duality; monotone operator; nonlinear composition; perturbation theory; proximal method; splitting algorithm
Sources: Web Of Science, NC State University Libraries
Added: January 2, 2024

2023 journal article

Resolvent and Proximal Compositions

SET-VALUED AND VARIATIONAL ANALYSIS, 31(3).

By: P. Combettes

author keywords: Monotone operator; Proximal average; Proximal composition; Proximal point algorithm; Relaxed monotone inclusion; Resolvent average; Resolvent composition; Resolvent mixture
UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science; OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: July 24, 2023

2022 journal article

A Variational Inequality Model for the Construction of Signals from Inconsistent Nonlinear Equations\ast

SIAM JOURNAL ON IMAGING SCIENCES, 15(1), 84–109.

By: P. Combettes* & Z. Woodstock

author keywords: image recovery; signal synthesis; monotone operator; nonlinear observation; firmly nonexpansive operator; variational inequality
TL;DR: It is proposed that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies a number of nonlinear equations involving firmly nonexpansive operators. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: March 21, 2022

2022 article

BLOCK-ACTIVATED ALGORITHMS FOR MULTICOMPONENT FULLY NONSMOOTH MINIMIZATION

2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), pp. 5428–5432.

By: M. Bui n, P. Combettes n & Z. Woodstock n

author keywords: Block-activated algorithm; image recovery; machine learning; nonsmooth convex minimization; proximal splitting
TL;DR: This work investigates the application of block-activated proximal algorithms for solving multicomponent minimization problems involving a separable nonsmooth convex function penalizing the components individually, and nonsm Smooth convex coupling terms penalizing linear mixtures of the components. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: January 9, 2023

2022 article

SIGNAL RECOVERY FROM INCONSISTENT NONLINEAR OBSERVATIONS

2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), pp. 5872–5876.

By: P. Combettes n & Z. Woodstock n

author keywords: Firmly nonexpansive operator; inconsistent nonlinear observations; signal recovery; variational inequality
TL;DR: To address problems with inaccurate measurements, this work proposes solving a variational inequality relaxation which is guaranteed to possess solutions under mild conditions and which coincides with the original problem if it happens to be consistent. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: January 9, 2023

2021 conference paper

A Fixed Point Framework for Recovering Signals from Nonlinear Transformations

2020 28th European Signal Processing Conference (EUSIPCO), 2120–2124.

By: P. Combettes n & Z. Woodstock n

Event: 2020 28th European Signal Processing Conference (EUSIPCO) at Amsterdam, Netherlands on January 18-21, 2021

TL;DR: The problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information, is considered and the recovery problem is reduced to a tractable common fixed point formulation, which is solved efficiently by a provably convergent, block-iterative algorithm. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: November 5, 2021

2021 report

Analysis and numerical solution of a modular convex Nash equilibrium problem

(HAL Preprint No. hal-03412172). https://hal.archives-ouvertes.fr/hal-03412172

By: M. Bùi & P. Combettes

Source: NC State University Libraries
Added: November 10, 2021

2021 report

Block-Activated Algorithms for Multicomponent Fully Nonsmooth Minimization

(ArXiv Preprint No. 2103.00520).

By: M. Bùi, P. Combettes* & Z. Woodstock

Sources: Crossref, NC State University Libraries
Added: October 31, 2023

2021 journal article

Bregman Forward-Backward Operator Splitting

Set-Valued and Variational Analysis, 29(3), 583–603.

By: M. Bui n & P. Combettes n

author keywords: Banach space; Bregman distance; Forward-backward splitting; Legendre function; Monotone operator
Sources: Web Of Science, ORCID, NC State University Libraries
Added: December 21, 2020

2021 journal article

Fixed Point Strategies in Data Science

IEEE Transactions on Signal Processing, 69, 3878–3905.

By: P. Combettes n & J. Pesquet

author keywords: Data science; Tools; Signal processing algorithms; Inverse problems; Convex functions; Standards; Neural networks; Convex optimization; fixed point; game theory; image recovery; inverse problems; machine learning; monotone inclusion; neural networks; nonexpansive operator; signal processing
TL;DR: Fixed point strategies are seen to constitute a natural environment to explain the behavior of advanced convex optimization methods as well as of recent nonlinear methods in data science which are formulated in terms of paradigms that go beyond minimization concepts and involve constructs such as Nash equilibria or monotone inclusions. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 16, 2021

2021 article

Multivariate Monotone Inclusions in Saddle Form

Bui, M. N., & Combettes, P. L. (2021, December 21). MATHEMATICS OF OPERATIONS RESEARCH, Vol. 12.

By: M. Bui n & P. Combettes n

author keywords: monotone inclusion; monotone operator; saddle form; operator splitting; block-iterative algorithm; asynchronous algorithm; strong convergence
TL;DR: A novel approach to monotone operator splitting based on the notion of a saddle operator, which achieves full splitting, exploits the specific attributes of each operator, is asynchronous, and requires to activate only blocks of operators at each iteration, as opposed to activating all of them. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science; OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: January 10, 2022

2021 journal article

Reconstruction of functions from prescribed proximal points

Journal of Approximation Theory, 268, 105606.

By: P. Combettes n & Z. Woodstock n

author keywords: Best approximation algorithm; Constrained interpolation; Firmly nonexpansive operator; Nonlinear signal recovery; Proximal point
TL;DR: This work shows that in many instances these prescriptions can be represented using firmly nonexpansive operators, even when the original observation process is discontinuous, and captures a large body of classical and contemporary best approximation problems arising in areas such as harmonic analysis, statistics, interpolation theory, and signal processing. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: July 12, 2021

2021 journal article

Regression Models for Compositional Data: General Log-Contrast Formulations, Proximal Optimization, and Microbiome Data Applications

Statistics in Biosciences, 13(2), 217–242.

By: P. Combettes n & C. Mueller

author keywords: Compositional data; Convex optimization; Log-contrast model; Microbiome; Perspective function; Proximal algorithm
TL;DR: A general convex optimization model for linear log-contrast regression which includes many previous proposals as special cases is proposed and a proximal algorithm is introduced that solves the resulting constrained optimization problem exactly with rigorous convergence guarantees. (via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: Web Of Science, Crossref, NC State University Libraries
Added: July 6, 2020

2021 journal article

Solving Composite Fixed Point Problems with Block Updates

Advances in Nonlinear Analysis, 10(1), 1154–1177.

By: P. Combettes n & L. Glaudin*

author keywords: averaged operator; constrained minimization; forward-backward splitting; fixed point iterations; monotone operator; nonexpansive operator; variational inequality
TL;DR: Applications to several nonlinear and nonsmooth analysis problems are presented, ranging from monotone inclusions and inconsistent feasibility problems, to variational inequalities and minimization problems arising in data science. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: May 17, 2021

2020 journal article

Deep Neural Network Structures Solving Variational Inequalities

Set-Valued and Variational Analysis, 28(3), 491–518.

By: P. Combettes n & J. Pesquet

author keywords: Averaged operator; Deep neural network; Monotone operator; Nonexpansive operator; Proximity operator; Variational inequality
TL;DR: It is shown that the limit of the resulting process solves a variational inequality which, in general, does not derive from a minimization problem. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science; OpenAlex)
Sources: Web Of Science, Crossref, NC State University Libraries
Added: August 17, 2020

2020 journal article

Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operators

SIAM Journal on Mathematics of Data Science, 2(2), 529–557.

By: P. Combettes* & J. Pesquet

author keywords: activation function; neural network; nonexpansive operator; averaged operator; stability; layered network
TL;DR: This work derives sharp Lipschitz constants for feed-forward neural networks from the context of convolutional neural networks to assess their robustness in the face of perturbations of their inputs. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries, Web Of Science
Added: September 9, 2020

2020 journal article

Perspective maximum likelihood-type estimation via proximal decomposition

Electronic Journal of Statistics, 14(1), 207–238.

By: P. Combettes* & C. Müller

author keywords: Convex optimization; heteroscedastic model; concomitant M-estimator; perspective function; proximal algorithm; robust regression
TL;DR: An optimization model for maximum likelihood-type estimation (M-estimation) that generalizes a large class of existing statistical models, including Huber's concomitant M-estimator, Owen's Huber/Berhu concomant estimator, the scaled lasso, support vector machine regression, and penalized estimation with structured sparsity is introduced. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, Crossref, NC State University Libraries
Added: August 3, 2020

2020 journal article

The Douglas--Rachford Algorithm Converges Only Weakly

SIAM Journal on Control and Optimization, 58(2), 1118–1120.

By: M. Bùi* & P. Combettes*

author keywords: Douglas-Rachford algorithm; method of partial inverses; monotone operator; operator splitting; strong convergence
TL;DR: It is shown that the weak convergence of the Douglas--Rachford algorithm for finding a zero of the sum of two maximally monotone operators cannot be improved to strong convergence and strong convergence can fail for the method of partial inverses. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science)
Sources: Web Of Science, Crossref, NC State University Libraries
Added: July 20, 2020

2020 journal article

Warped proximal iterations for monotone inclusions

Journal of Mathematical Analysis and Applications, 491(1), 124315.

By: M. Bùi n & P. Combettes n

author keywords: Monotone inclusion; Operator splitting; Strong convergence; Warped resolvent; Warped proximal iterations
UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science; OpenAlex)
Sources: Web Of Science, Crossref, NC State University Libraries
Added: August 10, 2020

2019 conference paper

Fully Proximal Splitting Algorithms In Image Recovery

2019 27th European Signal Processing Conference (EUSIPCO). Presented at the 2019 27th European Signal Processing Conference (EUSIPCO), A Coruna, Spain.

By: P. Combettes n & L. Glaudin*

Event: 2019 27th European Signal Processing Conference (EUSIPCO) at A Coruna, Spain on September 2-6, 2019

TL;DR: It is shown that, although intuitively natural, the common practice is to activate the smooth functions via their gradient and the nonsmooth ones via their proximity operator, and that activating all the functions proximally may be advantageous. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: November 5, 2021

2019 journal article

Learning with optimal interpolation norms

Numerical Algorithms, 81(2), 695–717.

By: P. Combettes n, A. McDonald*, C. Micchelli* & M. Pontil*

author keywords: Block-coordinate proximal algorithm; Douglas-Rachford splitting; Infimal postcomposition; Latent group lasso; Machine learning; Optimal interpolation norm
TL;DR: A class of norms defined via an optimal interpolation problem involving the composition of norms and a linear operator is analyzed, shown to encompass various norms which have been used as regularizers in machine learning, signal processing, and statistics. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: June 17, 2019

2019 journal article

Proximal Activation of Smooth Functions in Splitting Algorithms for Convex Image Recovery

SIAM Journal on Imaging Sciences, 12(4), 1905–1935.

By: P. Combettes* & L. Glaudin

author keywords: convex optimization; image recovery; inconsistent convex feasibility problem; proximal splitting algorithm; proximity operator
TL;DR: A novel variational model to relax inconsistent convex feasibility problems is investigated within the proposed framework and several numerical applications to image recovery are presented to compare the behavior of fully proximal versus mixed proximal/gradient implementations of several splitting algorithms. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: July 20, 2020

2019 journal article

Stochastic quasi-Fejer block-coordinate fixed point iterations with random sweeping II: mean-square and linear convergence

Mathematical Programming, 174(1-2), 433–451.

By: P. Combettes n & J. Pesquet

author keywords: Block-coordinate algorithm; Fixed-point algorithm; Mean-square convergence; Monotone operator splitting; Linear convergence; Stochastic algorithm
TL;DR: Results on the mean-square and linear convergence of the iterates of the block-coordinate fixed point algorithms are established and applications to monotone operator splitting and proximal optimization algorithms are presented. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: April 22, 2019

2018 journal article

Consistent learning by composite proximal thresholding

MATHEMATICAL PROGRAMMING, 167(1), 99–127.

By: P. Combettes n, S. Salzo* & S. Villa*

author keywords: Consistent estimator; Convex optimization; Forward-backward splitting; Proximal algorithm; Sparse data representation
TL;DR: A novel flexible composite regularization model is proposed, which makes it possible to incorporate various priors on the coefficients of the prediction function, including sparsity and hard constraints, and an error-tolerant composite proximal thresholding algorithm is designed. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2018 conference paper

Linear convergence of stochastic block-coordinate fixed point algorithms

Proceedings of the European Signal Processing Conference, 747–751.

By: P. Combettes n & J. Pesquet

Event: European Signal Processing Conference at Rome, Italy on September 3-7, 2018

TL;DR: New linear convergence results are provided that are compared to those of standard deterministic algorithms both theoretically and experimentally in an image recovery problem. (via Semantic Scholar)
Sources: NC State University Libraries, NC State University Libraries
Added: September 29, 2019

2018 article

Monotone operator theory in convex optimization

Combettes, P. L. (2018, July). MATHEMATICAL PROGRAMMING, Vol. 170, pp. 177–206.

By: P. Combettes n

author keywords: Firmly nonexpansive operator; Monotone operator; Operator splitting; Proximal algorithm; Proximity operator; Proximity-preserving transformation; Self-dual class; Subdifferential
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2018 journal article

Perspective Functions: Properties, Constructions, and Examples

SET-VALUED AND VARIATIONAL ANALYSIS, 26(2), 247–264.

By: P. Combettes n

author keywords: Berhu function; Convex function; Convex optimization; Huber function; Integral functional; Perspective function; Statistical divergence
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2018 journal article

Perspective functions: Proximal calculus and applications in high-dimensional statistics

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 457(2), 1283–1306.

By: P. Combettes n & C. Muller*

author keywords: Convex function; Perspective function; Proximal algorithm; Proximity operator; Statistics
TL;DR: It is shown that proximal methods provide an efficient framework to model and solve problems involving perspective functions and showcases the versatility of the framework by designing novel proximal algorithms for state-of-the-art regression and variable selection schemes in high-dimensional statistics. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2018 journal article

Regularized learning schemes in feature Banach spaces

ANALYSIS AND APPLICATIONS, 16(1), 1–54.

By: P. Combettes n, S. Salzo* & S. Villa*

author keywords: Consistency; Banach spaces; empirical risk; feature map; reproducing kernel; regularization; representer theorem; statistical learning; totally convex function
TL;DR: A unified framework for the investigation of constrained learning theory in reflexive Banach spaces of features via regularized empirical risk minimization with totally convex functions is proposed, which establishes a new general form of the representer theorem and the consistency of the corresponding learning schemes. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2017 journal article

Classification and Regression Using an Outer Approximation Projection-Gradient Method

IEEE TRANSACTIONS ON SIGNAL PROCESSING, 65(17), 4635–4644.

By: M. Barlaud*, W. Belhajali*, P. Combettes n & L. Fillatre*

author keywords: Convex optimization; outer approximation; projection-gradient algorithm
TL;DR: Convergence of the iterates generated by the algorithm is established for a general smooth convex minimization problem with inequality constraints and experiments show that the method outperforms penalty methods. (via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2017 book

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

In CMS Books in Mathematics (2nd ed.).

By: H. Bauschke* & P. Combettes*

UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 20, 2019

2017 journal article

QUASI-NONEXPANSIVE ITERATIONS ON THE AFFINE HULL OF ORBITS: FROM MANN'S MEAN VALUE ALGORITHM TO INERTIAL METHODS

SIAM JOURNAL ON OPTIMIZATION, 27(4), 2356–2380.

By: P. Combettes n & L. Glaudin*

author keywords: averaged operator; fixed point iteration; forward-backward algorithm; inertial algorithm; mean value iterations; monotone operator splitting; nonsmooth minimization; Peaceman-Rachford algorithm; proximal algorithm
TL;DR: This investigation unifies several algorithmic constructs, including Mann's mean value method, inertial methods, and multilayer memoryless methods, which provides a framework for the development of new algorithms, such as those proposed for solving monotone inclusion and minimization problems. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2016 journal article

Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions

Mathematical Programming, 168(1-2), 645–672.

By: P. Combettes* & J. Eckstein*

author keywords: Asynchronous algorithm; Block-iterative algorithm; Duality; Monotone inclusion; Monotone operator; Primal-dual algorithm; Splitting algorithm
TL;DR: This work proposes new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators, and presents two related methods: the first method provides weakly convergent primal and dual sequences under general conditions, while the second is a variant in which strong convergence is guaranteed without additional assumptions. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 20, 2019

2016 journal article

Solving composite monotone inclusions in reflexive Banach spaces by constructing best Bregman approximations from their Kuhn-Tucker set

Journal of Convex Analysis, 23(2), 481–510.

By: P. Combettes & Q. Nguyen

Source: NC State University Libraries
Added: August 29, 2019

2016 journal article

Stochastic approximations and perturbations in forward-backward splitting for monotone operators

Pure and Applied Functional Analysis, 1(1), 13–37. http://www.yokohamapublishers.jp/online2/oppafa/vol1/p13.html

By: P. Combettes & J. Pesquet

Contributors: P. Combettes

Sources: NC State University Libraries, ORCID
Added: July 10, 2019

2016 conference paper

Stochastic forward-backward and primal-dual approximation algorithms with application to online image restoration

Proceedings of the European Signal Processing Conference. Presented at the Proceedings of the European Signal Processing Conference, Budapest, Hungary.

By: P. Combettes* & J. Pesquet*

Event: Proceedings of the European Signal Processing Conference at Budapest, Hungary on August 29 - September 2, 2016

TL;DR: A stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily smooth, which is proposed and established under relatively mild assumptions. (via Semantic Scholar)
Sources: NC State University Libraries, NC State University Libraries
Added: September 8, 2020

2015 journal article

A strongly convergent primal–dual method for nonoverlapping domain decomposition

Numerische Mathematik, 133(3), 443–470.

By: H. Attouch*, L. Briceño-Arias* & P. Combettes*

TL;DR: A primal–dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations, which can handle a wide range of linear and nonlinear problems, with flexible, possibly nonlinear, transmission conditions across the interfaces. (via Semantic Scholar)
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 20, 2019

2015 journal article

Best Approximation from the Kuhn-Tucker Set of Composite Monotone Inclusions

Numerical Functional Analysis and Optimization, 36(12), 1513–1532.

By: A. Alotaibi*, P. Combettes* & N. Shahzad*

author keywords: Best approximation; Duality; Haugazeau; Monotone operator; Primal-dual algorithm; Splitting algorithm; Strong convergence
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 20, 2019

2015 journal article

Compositions and convex combinations of averaged nonexpansive operators

Journal of Mathematical Analysis and Applications, 425(1), 55–70.

By: P. Combettes* & I. Yamada*

author keywords: Averaged operator; Fixed-point algorithm; Forward-backward splitting; Monotone operator; Nonexpansive operator
Sources: Crossref, NC State University Libraries
Added: July 20, 2019

2015 journal article

Kolmogorov n-Widths of Function Classes Induced by a Non-Degenerate Differential Operator: A Convex Duality Approach

Set-Valued and Variational Analysis, 24(1), 83–99.

By: P. Combettes* & D. Dũng*

author keywords: Asymptotic order; Kolmogorov n-widths; Non-degenerate differential operator; Convex duality
Sources: Crossref, NC State University Libraries
Added: July 20, 2019

2015 journal article

Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping

SIAM Journal on Optimization, 25(2), 1221–1248.

By: P. Combettes* & J. Pesquet*

author keywords: arbitrary sampling; block-coordinate algorithm; fixed-point algorithm; monotone operator splitting; primal-dual algorithm; stochastic quasi-Fejer sequence; stochastic algorithm; structured convex minimization problem
TL;DR: This work proposes block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces and relies on a notion of stochastic quasi-Fejer monotonicity for its asymptotic analysis. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 20, 2019

2014 conference paper

A forward-backward view of some primal-dual optimization methods in image recovery

Proceedings of the IEEE International Conference on Image Processing, 4141–4145.

By: P. Combettes*, L. Condat*, J. Pesquet* & B. Vũ*

Event: Proceedings of the IEEE International Conference on Image Processing at Paris, France on October 27-30, 2014

TL;DR: The objective of this paper is to show that a number of existing algorithms can be derived from a general form of the forward-backward algorithm applied in a suitable product space, and to develop useful extensions ofexisting algorithms by introducing a variable metric. (via Semantic Scholar)
Sources: NC State University Libraries, NC State University Libraries
Added: September 8, 2020

2014 journal article

A primal-dual method of partial inverses for composite inclusions

Optimization Letters, 8(8), 2271–2284.

By: M. Alghamdi, A. Alotaibi, P. Combettes* & N. Shahzad

author keywords: Convex optimization; Duality; Method of partial inverses; Monotone operator; Splitting algorithm
TL;DR: It is shown that Spingarn's method of partial inverses can be employed to solve composite monotone inclusions in duality, thus opening a new range of applications for the partial inverse formalism. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 20, 2019

2014 journal article

An algorithm for splitting parallel sums of linearly composed monotone operators, with applications to signal recovery

Journal of Nonlinear and Convex Analysis, 15(1), 137–159.

By: S. Becker & P. Combettes

Source: NC State University Libraries
Added: August 29, 2019

2014 journal article

Asymptotic behavior of compositions of under-relaxed nonexpansive operators

Journal of Dynamics and Games, 1(3), 331–346.

By: J. Baillon*, P. Combettes* & R. Cominetti*

author keywords: Cyclic projections; De Pierro's conjecture; fixed point; nonexpansive operator; projection operator; under-relaxed cycles
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2014 journal article

Modern convex analysis

Mathematical Programming, 148, 1–4.

By: P. Combettes*, J. Hiriart-Urruty* & M. Théra*

Sources: Web Of Science, NC State University Libraries
Added: September 8, 2020

2014 journal article

Solving Coupled Composite Monotone Inclusions by Successive Fejér Approximations of their Kuhn--Tucker Set

SIAM Journal on Optimization, 24(4), 2076–2095.

By: A. Alotaibi, P. Combettes* & N. Shahzad

author keywords: duality; Fejer monotonicity; monotone inclusion; monotone operator; primal-dual algorithm; splitting algorithm
TL;DR: A new class of primal-dual Fejermonotone algorithms for solving systems of composite monotone inclusions that do not require prior knowledge of bounds on the linear operators involved or the inversion of linear operators. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 20, 2019

2013 chapter

Monotone Operator Methods for Nash Equilibria in Non-potential Games

In Computational and Analytical Mathematics (pp. 143–159).

By: L. Briceño-Arias* & P. Combettes*

author keywords: Monotone operator; Nash equilibrium; Potential game; Proximal algorithm; Splitting method; Zero-sum game
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019

2013 journal article

Moreau’s decomposition in Banach spaces

Mathematical Programming, 139(1-2), 103–114.

By: P. Combettes* & N. Reyes*

author keywords: Banach space; Bregman distance; Convex optimization; Infimal convolution; Legendre function; Moreau's decomposition; Proximity operator
Sources: Crossref, NC State University Libraries
Added: July 27, 2019

2013 journal article

Systems of Structured Monotone Inclusions: Duality, Algorithms, and Applications

SIAM Journal on Optimization, 23(4), 2420–2447.

By: P. Combettes*

author keywords: convex minimization; coupled system; infimal convolution; monotone inclusion; monotone operator; operator splitting; parallel algorithm; structured minimization problem
TL;DR: A general primal-dual splitting algorithm for solving systems of structured coupled monotone inclusions in Hilbert spaces is introduced and its asymptotic behavior is analyzed, providing a flexible solution method applicable to a variety of problems beyond the reach of the state-of-the-art. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019

2013 journal article

Variable metric quasi-Fejér monotonicity

Nonlinear Analysis: Theory, Methods & Applications, 78, 17–31.

By: P. Combettes* & B. Vũ*

author keywords: Convex feasibility problem; Convex optimization; Hilbert space; Inverse problems; Proximal Landweber method; Proximal point algorithm; Quasi-Fejer sequence; Variable metric
TL;DR: This paper extends the notion of quasi-Fejer monotonicity in the context of variable metric algorithms, whereby the underlying norm is allowed to vary at each iteration. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019

2012 journal article

There is no variational characterization of the cycles in the method of periodic projections

Journal of Functional Analysis, 262(1), 400–408.

By: J. Baillon, P. Combettes* & R. Cominetti

author keywords: Alternating projections; Best approximation; Limit cycle; Von Neumann algorithm
Sources: Crossref, NC State University Libraries
Added: July 27, 2019

2012 journal article

Variable metric forward–backward splitting with applications to monotone inclusions in duality

Optimization, 63(9), 1289–1318.

By: P. Combettes* & B. Vũ*

author keywords: cocoercive operator; composite operator; demiregularity; duality; forward-backward splitting algorithm; monotone inclusion; monotone operator; primal-dual algorithm; quasi-Fejer sequence; variable metric
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 20, 2019

2011 journal article

A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality

SIAM Journal on Optimization, 21(4), 1230–1250.

By: L. Briceño-Arias* & P. Combettes*

author keywords: composite operator; convex optimization; decomposition; duality; Fenchel-Rockafellar duality; forward-backward-forward algorithm; minimization algorithm; monotone inclusion; monotone operator; operator splitting
TL;DR: The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximallymonotone operator and a linear skew-adjoint operator. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2011 book

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

In CMS Books in Mathematics.

By: H. Bauschke* & P. Combettes*

TL;DR: This book provides a largely self-contained account of the main results of convex analysis and optimization in Hilbert space, and a concise exposition of related constructive fixed point theory that allows for a wide range of algorithms to construct solutions to problems in optimization, equilibrium theory, monotone inclusions, variational inequalities, and convex feasibility. (via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: July 27, 2019

2011 book

Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Patrick Combettes

Ed(s): H. Bauschke, R. Burachik, P. Combettes*, V. Elser, D. Luke & H. Wolkowicz

TL;DR: The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019

2011 journal article

On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints

Computational Optimization and Applications, 51(3), 1065–1088.

By: Y. Censor*, W. Chen*, P. Combettes*, R. Davidi* & G. Herman*

author keywords: Projection methods; Convex feasibility problems; Numerical evaluation; Optimization; Linear inequalities; Sparse matrices
TL;DR: It is shown that projection methods often have a computational advantage over alternatives that have been proposed for solving the same problem and that this makes them successful in many real-world applications. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019

2011 journal article

Primal-Dual Splitting Algorithm for Solving Inclusions with Mixtures of Composite, Lipschitzian, and Parallel-Sum Type Monotone Operators

Set-Valued and Variational Analysis, 20(2), 307–330.

By: P. Combettes* & J. Pesquet*

author keywords: Maximal monotone operator; Monotone inclusion; Nonsmooth convex optimization; Parallel sum; Set-valued duality; Splitting algorithm
TL;DR: This work brings together and notably extends various types of structured monotone inclusion problems and their solution methods and the application to convex minimization problems is given special attention. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019

2011 chapter

Proximal Splitting Methods in Signal Processing

In Springer Optimization and Its Applications (pp. 185–212).

By: P. Combettes* & J. Pesquet

author keywords: Alternating-direction method of multipliers; Backward-backward algorithm; Convex optimization; Denoising; Douglas-Rachford algorithm; Forward-backward algorithm; Frame; Landweber method; Iterative thresholding; Parallel computing; Peaceman-Rachford algorithm; Proximal algorithm; Restoration and reconstruction; Sparsity; Splitting
TL;DR: The basic properties of proximity operators which are relevant to signal processing and optimization methods based on these operators are reviewed and proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2011 journal article

Proximity for sums of composite functions

Journal of Mathematical Analysis and Applications, 380(2), 680–688.

By: P. Combettes*, Đ. Dũng* & B. Vũ*

author keywords: Best approximation; Convex optimization; Duality; Image recovery; Proximity operator; Proximal splitting algorithm; Elastic net
TL;DR: An algorithm for computing the proximity operator of a sum of composite convex functions in Hilbert spaces and investigating its asymptotic behavior to best approximation and image recovery are proposed. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2010 journal article

A Parallel Splitting Method for Coupled Monotone Inclusions

SIAM Journal on Control and Optimization, 48(5), 3246–3270.

By: H. Attouch*, L. Briceño-Arias* & P. Combettes*

author keywords: coupled systems; demiregular operator; evolution inclusion; forward-backward algorithm; maximal monotone operator; operator splitting; parallel algorithm; weak convergence
TL;DR: A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces, and its convergence is established under the assumption that solutions exist. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2010 conference paper

Alternating proximal algorithm for blind image recovery

Proceedings of the IEEE International Conference on Image Processing, 1673–1676.

By: J. Bolte, P. Combettes* & J. Pesquet*

Event: Proceedings of the IEEE International Conference on Image Processing at Hong Kong on September 26-29, 2010

author keywords: Blind restoration; blind reconstruction; proximal methods; nonlinear optimization; wavelets
TL;DR: A novel iterative proximal algorithm is proposed to solve the associated nonconvex minimization problem and is shown to have better convergence properties than standard alternating minimization techniques. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: September 8, 2020

2010 journal article

Dualization of Signal Recovery Problems

Set-Valued and Variational Analysis, 18(3-4), 373–404.

By: P. Combettes*, Đ. Dũng* & B. Vũ*

author keywords: Convex optimization; Denoising; Dictionary; Dykstra-like algorithm; Duality; Forward-backward splitting; Image reconstruction; Image restoration; Inverse problem; Signal recovery; Primal-dual algorithm; Proximity operator; Total variation
TL;DR: This framework is shown to capture and extend several existing duality-based signal recovery methods and to be applicable to a variety of new problems beyond their scope. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2010 journal article

Functions with prescribed best linear approximations

Journal of Approximation Theory, 162(5), 1095–1116.

By: P. Combettes* & N. Reyes*

TL;DR: This paper provides various characterizations of the Inverse Best Approximation Property (IBAP) in terms of the geometry of the subspaces and links between the IBAP and the linear convergence rate of the periodic projection algorithm for solving the underlying affine feasibility problem are established. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2010 journal article

Proximal Algorithms for Multicomponent Image Recovery Problems

Journal of Mathematical Imaging and Vision, 41(1-2), 3–22.

By: L. Briceño-Arias*, P. Combettes*, J. Pesquet* & N. Pustelnik*

author keywords: Convex minimization; Image recovery; Inverse problems; Multicomponent images; Multichannel images; Multispectral images; Proximal algorithm; Sparsity; Stereoscopy; Wavelets
TL;DR: This paper first provides closed form expressions for several important multicomponent proximity operators and then derive extensions of existing proximal algorithms to the multicomponents setting that are applied to stereoscopic image recovery, multispectral image denoising, and image decomposition into texture and geometry components. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2010 conference paper

Proximal method for geometry and texture image decomposition

Proceedings of the IEEE International Conference on Image Processing, 2721–2724.

By: L. Briceño-Arias*, P. Combettes*, J. Pesquet* & N. Pustelnik*

Event: Proceedings of the IEEE International Conference on Image Processing at Hong Kong on September 26-29, 2010

author keywords: Convex optimization; denoising; image decomposition; image restoration; proximity operator
TL;DR: A variational method for decomposing an image into a geometry and a texture component that involves the sum of two functions promoting separately properties of each component, and of a coupling function modeling the interaction between the components. (via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: September 8, 2020

2010 journal article

The Baillon-Haddad theorem revisited

Journal of Convex Analysis, 17(4), 781–787.

By: H. Bauschke & P. Combettes

Source: NC State University Libraries
Added: July 10, 2019

2009 journal article

Convex variational formulation with smooth coupling for multicomponent signal decomposition and recovery

Numerical Mathematics: Theory, Methods, and Applications, 2(4), 485–508.

By: L. Briceño-Arias* & P. Combettes

author keywords: Convex optimization; denoising; image restoration; proximal algorithm; signal decomposition; signal recovery
TL;DR: A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert spaces and an algorithm with guaranteed weak convergence to a solution to the problem is provided. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 29, 2019

2009 journal article

Iterative construction of the resolvent of a sum of maximal monotone operators

Journal of Convex Analysis, 16(4), 727–748.

By: P. Combettes

Source: NC State University Libraries
Added: August 29, 2019

2009 conference paper

Split convex minimization algorithm for signal recovery

Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 685–688.

By: P. Combettes* & J. Pesquet*

Event: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing at Taipei, Taiwan on April 19-24, 2009

author keywords: convex optimization methods; inverse problems; parallel algorithm; signal restoration; variational methods; wavelet transforms
TL;DR: This work proposes a proximal decomposition algorithm which, under mild conditions, provides a solution to the problem of minimizing the sum of several convex functions in a Hilbert space. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: September 8, 2020

2008 chapter

A Convex Programming Algorithm for Noisy Discrete Tomography

In Advances in Discrete Tomography and Its Applications (pp. 207–226).

By: T. Capricelli* & P. Combettes*

TL;DR: A convex programming approach to discrete tomographic image reconstruction in noisy environments is proposed, with conventional constraints mixed with noise-based constraints on the sinogram and a binariness-promoting total variation constraint. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2008 journal article

A Dykstra-like algorithm for two monotone operators

Pacific Journal of Optimization, 4(3), 383–391.

By: H. Bauschke & P. Combettes

Source: NC State University Libraries
Added: September 9, 2019

2008 journal article

A proximal decomposition method for solving convex variational inverse problems

Inverse Problems, 24(6), 065014.

By: P. Combettes* & J. Pesquet*

TL;DR: A proximal decomposition algorithm for solving the problem of minimizing the sum of several convex functions in a Hilbert space with an arbitrary number of nonsmooth functions is proposed and established. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2008 journal article

Proximal Thresholding Algorithm for Minimization over Orthonormal Bases

SIAM Journal on Optimization, 18(4), 1351–1376.

By: P. Combettes* & J. Pesquet

author keywords: convex programming; deconvolution; denoising; forward-backward splitting algorithm; Hilbert space; orthonormal basis; proximal algorithm; proximal thresholding; proximity operator; signal recovery; soft thresholding; strong convergence
TL;DR: This work proposes a versatile convex variational formulation for optimization over orthonormal bases that covers a wide range of problems, and establishes the strong convergence of a proximal thresholding algorithm to solve it. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2008 journal article

Visco-penalization of the sum of two monotone operators

Nonlinear Analysis: Theory, Methods & Applications, 69(2), 579–591.

By: P. Combettes* & S. Hirstoaga*

author keywords: approximating curve; monotone operator; penalization; variational inequality; viscosity; Yosida approximation
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2007 journal article

A Douglas–Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery

IEEE Journal of Selected Topics in Signal Processing, 1(4), 564–574.

By: P. Combettes* & J. Pesquet*

author keywords: Convex optimization; denoising; Douglas-Rachford; frame; nondifferentiable optimization; Poisson noise; proximal algorithm; wavelets
TL;DR: A decomposition method based on the Douglas-Rachford algorithm for monotone operator-splitting for signal recovery problems and applications to non-Gaussian image denoising in a tight frame are demonstrated. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2007 journal article

A variational formulation for frame-based inverse problems

Inverse Problems, 23(4), 1495–1518.

By: C. Chaux*, P. Combettes*, J. Pesquet* & V. Wajs*

TL;DR: A splitting algorithm is presented to solve this problem and its convergence is established in infinite-dimensional spaces under mild conditions on the penalization functions, which need not be differentiable. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2007 conference paper

Opérateurs proximaux pour la restauration bayésienne de signaux

Proceedings of the Twenty First GRETSI Symposium, 1277–1280. http://hdl.handle.net/2042/17744

By: C. Chaux, P. Combettes, J. Pesquet & V. Wajs

Event: Proceedings of the Twenty First GRETSI Symposium at Troyes, France on September 11-14, 2007

Source: NC State University Libraries
Added: September 8, 2020

2007 conference paper

Sparse signal recovery by iterative proximal thresholding

Proceedings of the European Signal Processing Conference. Presented at the European Signal Processing Conference, Poznan, Poland.

By: P. Combettes & J. Pesquet

Event: European Signal Processing Conference at Poznan, Poland on September 3-7, 2007

Source: NC State University Libraries
Added: September 8, 2020

2006 conference paper

A decomposition method for nonsmooth convex variational signal recovery

Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 5, 989–992.

By: H. Bauschke*, P. Combettes* & J. Pesquet*

Event: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing at Toulouse, France on May 14-19, 2006

Sources: NC State University Libraries, NC State University Libraries
Added: September 8, 2020

2006 journal article

A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space

Journal of Approximation Theory, 141(1), 63–69.

By: H. Bauschke*, P. Combettes* & D. Luke*

author keywords: best approximation problem; convex set; projection; strong convergence
TL;DR: A new iterative method for finding the projection onto the intersection of two closed convex sets in a Hilbert space is presented, a Haugazeau-like modification of a recently proposed averaged alternating reflections method which produces a strongly convergent sequence. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2006 journal article

Approximating curves for nonexpansive and monotone operators

Journal of Convex Analysis, 13(3-4), 633–646.

By: P. Combettes & S. Hirstoaga

Source: NC State University Libraries
Added: September 9, 2019

2006 conference paper

Iterative image deconvolution using overcomplete representations

Proceedings of the European Signal Processing Conference. Presented at the 14th European Signal Processing Conference, Florence, Italy.

By: C. Chaux, P. Combettes, J. Pesquet & V. Wajs

Event: 14th European Signal Processing Conference at Florence, Italy on September 4-8, 2006

Source: NC State University Libraries
Added: September 8, 2020

2006 journal article

Joint minimization with alternating Bregman proximity operators

Pacific Journal of Optimization, 2(3), 401–424.

By: H. Bauschke, P. Combettes & D. Noll

Source: NC State University Libraries
Added: July 10, 2019

2005 conference paper

A forward-backward algorithm for image restoration with sparse representations

Proceedings of the International Conference on Signal Processing with Adaptative Sparse Structured Representations, 49–52.

By: C. Chaux, P. Combettes, J. Pesquet & V. Wajs

Event: Proceedings of the International Conference on Signal Processing with Adaptative Sparse Structured Representations at Rennes, France on November 16-18, 2005

Source: NC State University Libraries
Added: September 8, 2020

2005 conference paper

A new generation of iterative transform algorithms for phase contrast tomography

Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 4, 89–92.

By: H. Bauschke, P. Combettes* & D. Luke

Event: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing at Philadelphia, PA on March 19-23, 2005

TL;DR: The theory of convex optimisation is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval, and a relaxation of averaged alternating reflectors is proposed to determine the fundamental mathematical properties of the related operator in the convex case. (via Semantic Scholar)
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy (OpenAlex)
Sources: NC State University Libraries, NC State University Libraries
Added: September 8, 2020

2005 journal article

Equilibrium programming in Hilbert spaces

Journal of Nonlinear and Convex Analysis, 6(1), 117–136.

By: P. Combettes & S. Hirstoaga

Source: NC State University Libraries
Added: September 9, 2019

2005 conference paper

Estimating first-order finite-difference information in image restoration problems

2004 International Conference on Image Processing, 2004. ICIP '04. Presented at the 2004 International Conference on Image Processing, 2004. ICIP '04., Singapore.

By: P. Combettes* & J. Pesquet*

Event: 2004 International Conference on Image Processing, 2004. ICIP '04. at Singapore on October 24-27, 2004

TL;DR: A new statistical framework is proposed in which certain attributes of the finite-difference images are estimated a posteriori from the observed data under the assumption that the noise is additive and Gaussian. (via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: November 16, 2019

2005 journal article

Extrapolation algorithm for affine-convex feasibility problems

Numerical Algorithms, 41(3), 239–274.

By: H. Bauschke*, P. Combettes* & S. Kruk*

author keywords: affinite sets; convex feasibility problem; convex sets; extrapolation; Hilbert space; projection method
TL;DR: A general parallel block-iterative algorithmic framework in which the affine subspaces are exploited to introduce extrapolated over-relaxations is proposed, which encompasses a wide range of projection, subgradient projection, proximal, and fixed point methods encountered in various branches of applied mathematics. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2005 journal article

Parallel Block-Iterative Reconstruction Algorithms for Binary Tomography

Electronic Notes in Discrete Mathematics, 20, 263–280.

By: T. Capricelli* & P. Combettes*

TL;DR: A convex programming approach to binary tomographic image reconstruction in noisy environments is proposed, which involves conventional constraints being mixed with new constraints on the sinogram. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: November 16, 2019

2005 journal article

Signal Recovery by Proximal Forward-Backward Splitting

Multiscale Modeling & Simulation, 4(4), 1168–1200.

By: P. Combettes* & V. Wajs

TL;DR: It is shown that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties, which makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2005 journal article

The asymptotic behavior of the composition of two resolvents

Nonlinear Analysis: Theory, Methods & Applications, 60(2), 283–301.

By: H. Bauschke*, P. Combettes* & S. Reich*

author keywords: duality; firmly nonexpansive operator; gradient projection method; Hilbert space; monotone inclusion; monotone operator; proximal iteration; resolvent
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2005 journal article

The asymptotic behavior of the composition of two resolvents

Nonlinear Analysis, 60(2), 283–301.

By: H. Bauschke*, P. Combettes* & S. Reich*

UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 8, 2020

2005 conference paper

Theoretical analysis of some regularized image denoising methods

2004 International Conference on Image Processing, 2004. ICIP '04. Presented at the 2004 International Conference on Image Processing, 2004. ICIP '04., Singapore.

By: P. Combettes* & V. Wajs*

Event: 2004 International Conference on Image Processing, 2004. ICIP '04. at Singapore on October 24-27, 2004

TL;DR: A new synthetic approach to the study of regularization methods in image denoising problems based on Moreau's proximity operators is proposed, exploiting the remarkable properties enjoyed by these operators to establish in a systematic fashion a variety of properties of regularized denoizing problems. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: November 16, 2019

2005 conference paper

Éclatement des contraintes en reconstruction tomographique

Capricelli, T. D., & Combettes, P. L. (2005, September 6). Presented at the Actes du Vingtième Colloque GRETSI sur le Traitement du Signal et des Images, Louvain-la-Neuve, Belgium.

By: T. Capricelli & P. Combettes

Event: Actes du Vingtième Colloque GRETSI sur le Traitement du Signal et des Images at Louvain-la-Neuve, Belgium on September 6-9, 2005

Source: NC State University Libraries
Added: September 8, 2020

2004 conference paper

Constraint construction in convex set theoretic signal recovery via Stein's principle [image denoising example]

2004 IEEE International Conference on Acoustics, Speech, and Signal Processing. Presented at the 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing, Montreal, Quebec, Canada.

By: P. Combettes* & J. Pesquet*

Event: 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing at Montreal, Quebec, Canada on May 17-21, 2004

TL;DR: A new technique to construct constraint sets from probabilistic information based on Stein's identity is proposed, applicable to signal formation models involving additive Gaussian noise and it leads to geometrically simple sets that can easily be handled via projection methods. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: November 17, 2019

2004 journal article

Finding best approximation pairs relative to two closed convex sets in Hilbert spaces

Journal of Approximation Theory, 127(2), 178–192.

By: H. Bauschke, P. Combettes* & D. Luke

author keywords: best approximation pair; convex set; firmly nonexpansive map; Hilbert space; hybrid projection-reflection method; method of partial inverses; normal cone; projection; reflection; weak convergence
TL;DR: This work investigates systematically the asymptotic behavior of AAR in the general case when the sets do not necessarily intersect and shows that the method produces best approximation pairs provided they exist. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2004 journal article

Image Restoration Subject to a Total Variation Constraint

IEEE Transactions on Image Processing, 13(9), 1213–1222.

By: P. Combettes* & J. Pesquet*

MeSH headings : Algorithms; Computer Graphics; Computer Simulation; Image Enhancement / methods; Image Interpretation, Computer-Assisted / methods; Information Storage and Retrieval / methods; Models, Statistical; Numerical Analysis, Computer-Assisted; Pattern Recognition, Automated; Reproducibility of Results; Sensitivity and Specificity; Signal Processing, Computer-Assisted; Subtraction Technique
TL;DR: An alternative formulation in which total variation is used as a constraint in a general convex programming framework is proposed, which places no limitation on the incorporation of additional constraints in the restoration process and the resulting optimization problem can be solved efficiently via block-iterative methods. (via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2004 journal article

Proximal Methods for Cohypomonotone Operators

SIAM Journal on Control and Optimization, 43(2), 731–742.

By: P. Combettes* & T. Pennanen

author keywords: cohypomonotone operator; common zero problem; hypomonotone operator; method of multipliers; nonlinear programming; proximal point method; weak convergence
TL;DR: Conditions are given for the viability and the weak convergence of an inexact, relaxed proximal point algorithm for finding a common zero of countably many cohypomonotone operators in a Hilbert space. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2004 journal article

Solving monotone inclusions via compositions of nonexpansive averaged operators

Optimization, 53(5-6), 475–504.

By: P. Combettes*

author keywords: averaged operator; Douglas-Rach ford method; forward-backward method; monotone inclusion; monotone operator; proximal point algorithm
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2004 conference paper

Total variation information in image recovery

Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429). Presented at the International Conference on Image Processing, Barcelona, Spain.

By: P. Combettes* & J. Pesquet*

Event: International Conference on Image Processing at Barcelona, Spain on September 14-17, 2003

TL;DR: This paper proposes an alternative framework in which total variation is used as a constraint in a general quadratic programming context, which allows for a wider range of constraints to be easily incorporated in the recovery process. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: November 17, 2019

2004 journal article

Wavelet-constrained image restoration

International Journal of Wavelets, Multiresolution and Information Processing, 2(4), 371–389.

By: P. Combettes* & J. Pesquet*

TL;DR: Using a mix of statistical and convex-analytical tools, a general framework to construct wavelet-based constraints is proposed and the resulting optimization problem is solved with a block-iterative parallel algorithm which offers great flexibility in terms of implementation. (via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 18, 2019

2003 journal article

A block-iterative surrogate constraint splitting method for quadratic signal recovery

IEEE Transactions on Signal Processing, 51(7), 1771–1782.

By: P. Combettes*

author keywords: block-iterative optimization; convex analysis; deconvolution; quadratic programming; signal recovery; subgradient projection
TL;DR: A block-iterative parallel decomposition method is proposed to solve general quadratic signal recovery problems under convex constraints by local linearizations of blocks of constraints, and it is therefore not sensitive to their analytical complexity. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2003 journal article

Bregman Monotone Optimization Algorithms

SIAM Journal on Control and Optimization, 42(2), 596–636.

By: H. Bauschke*, J. Borwein* & P. Combettes*

author keywords: Banach space; block-iterative method; Bregman distance; Bregman monotone; Bregman projection; B-class operator; convex feasibility problem; essentially smooth function; essentially strict convex function; Fejer monotone; Legendre function; monotone operator; proximal mapping; proximal point algorithm; resolvent; subgradient projection
TL;DR: A systematic investigation of the notion of Bregman monotonicity leads to a simplified analysis of numerous algorithms and to the development of a new class of parallel block-iterative surrogate BRegman projection schemes. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2003 journal article

Construction of best Bregman approximations in reflexive Banach spaces

Proceedings of the American Mathematical Society, 131(12), 3757–3766.

By: H. Bauschke* & P. Combettes*

author keywords: best approximation; Bregman distance; decomposition; Haugazeau
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2003 journal article

Hybrid projection–reflection method for phase retrieval

Journal of the Optical Society of America A, 20(6), 1025.

By: H. Bauschke*, P. Combettes* & D. Luke*

TL;DR: A new projection-based method, termed the hybrid projection-reflection (HPR) algorithm, is introduced for solving phase-retrieval problems featuring nonnegativity constraints in the object domain, motivated by properties of the HPR algorithm for convex constraints. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2003 conference paper

Image deconvolution with total variation bounds

Seventh International Symposium on Signal Processing and Its Applications, 2003. Proceedings. Presented at the Seventh International Symposium on Signal Processing and Its Applications, Paris, France.

By: P. Combettes* & J. Pesquet*

Event: Seventh International Symposium on Signal Processing and Its Applications at Paris, France on July 4, 2003

TL;DR: An alternative framework in which total variation is used as a constraint is proposed, which places no limitation on the incorporation of additional constraints in the recovery process and can be solved efficiently via powerful block-iterative methods. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: November 17, 2019

2003 journal article

Iterating Bregman Retractions

SIAM Journal on Optimization, 13(4), 1159–1173.

By: H. Bauschke & P. Combettes*

author keywords: backward Bregman projection; Bregman distance; Bregman function; Bregman projection; Bregman retraction; convex feasibility problem; forward Bregman projection; Legendre function; paracontraction; projection algorithm
TL;DR: The main result on iterating Bregman retractions unifies several convergence results on projection methods for solving convex feasibility problems. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2003 conference paper

On the structure of some phase retrieval algorithms

Proceedings. International Conference on Image Processing. Presented at the ICIP 2002 International Conference on Image Processing, Rochester, New York.

By: H. Bauschke*, P. Combettes* & D. Luke*

Event: ICIP 2002 International Conference on Image Processing at Rochester, New York on September 22-25, 2002

TL;DR: It is shown that two other prominent phase retrieval methods also have well known counterparts in the world of convex optimization algorithms: Fienup's basic input-output algorithm corresponds to Dykstra's algorithm, and Fien up's hybrid input- Output algorithm can be viewed as an instance of the Douglas-Rachford algorithm. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: November 17, 2019

2002 conference paper

A block-iterative quadratic signal recovery algorithm

Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181). Presented at the 1998 IEEE International Conference on Acoustics, Speech, and Signal Processing, Seattle, Washington.

By: P. Combettes*

Event: 1998 IEEE International Conference on Acoustics, Speech, and Signal Processing at Seattle, Washington on May 15, 1998

TL;DR: A block-iterative parallel decomposition method to solve quadratic signal recovery problems under convex constraints by disintegrating the original multi-constraint problem into a sequence of simple quadRatic minimizations over the intersection of two half-spaces constructed by linearizing blocks of constraints. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: December 7, 2019

2002 conference paper

A level-set subgradient projection algorithm for non-differentiable signal restoration with multiple constraints

2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100). Presented at the 2000 International Conference on Acoustics, Speech and Signal Processing, Istanbul, Turkey.

By: J. Luo* & P. Combettes*

Event: 2000 International Conference on Acoustics, Speech and Signal Processing at Istanbul, Turkey on June 5-9, 2000

TL;DR: An new adaptive level-set subgradient projection algorithm is proposed to solve non-differentiable signal recovery problems with multiple convex constraints with constrained total variation signal restoration and denoising. (via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: December 7, 2019

2002 conference paper

A parallel constraint disintegration and approximation scheme for quadratic signal recovery

2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100). Presented at the 2000 International Conference on Acoustics, Speech and Signal Processing, Istanbul, Turkey.

By: P. Combettes*

Event: 2000 International Conference on Acoustics, Speech and Signal Processing at Istanbul, Turkey on June 5-9, 2000

TL;DR: A block-iterative parallel decomposition method is proposed to solve general quadratic signal recovery problems under convex constraints by local linearizations of blocks of constraints and it is not sensitive to their analytical complexity. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: December 7, 2019

2002 journal article

An adaptive level set method for nondifferentiable constrained image recovery

IEEE Transactions on Image Processing, 11(11), 1295–1304.

By: P. Combettes* & J. Luo*

author keywords: image recovery; level set method; nondifferentiable optimization; reconstruction; restoration; total variation
TL;DR: This work proposes an adaptive level set method for nondifferentiable constrained image recovery and analyzes the asymptotic properties of the method. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2002 conference paper

Convex multiresolution analysis

Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96). Presented at the Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96), Paris, France.

By: P. Combettes* & J. Pesquet*

Event: Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96) at Paris, France on June 18-21, 1996

TL;DR: This work proposes an extension of this framework in which the linear projection operators are replaced by nonlinear retractions onto convex sets, chosen so as to provide a recursive, monotone signal approximation scheme. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: December 7, 2019

2002 conference paper

Convex set theoretic image recovery with inexact projection algorithms

Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205). Presented at the 2001 International Conference on Image Processing, Thessaloniki, Greece.

By: P. Combettes*

Event: 2001 International Conference on Image Processing at Thessaloniki, Greece on October 7-10, 2001

TL;DR: This analysis covers sequential, parallel, and block-iterative (subgradient) projection methods for consistent and inconsistent set theoretic image recovery problems and shows that parallel projection methods are more robust to errors than sequential methods such as the popular POCS (projection on to convex sets) algorithm. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: December 7, 2019

2002 journal article

Generalized Mann iterates for constructing fixed points in Hilbert spaces

Journal of Mathematical Analysis and Applications, 275(2), 521–536.

By: P. Combettes* & T. Pennanen

Sources: Crossref, NC State University Libraries
Added: July 28, 2019

2002 conference paper

Generalized convex set theoretic image recovery

Proceedings of 3rd IEEE International Conference on Image Processing. Presented at the 3rd IEEE International Conference on Image Processing, Lausanne, Switzerland.

By: P. Combettes*

Event: 3rd IEEE International Conference on Image Processing at Lausanne, Switzerland on September 19, 1996

TL;DR: A generalized product space formalism is introduced, through which constraints that are convex in different Hilbert spaces can be combined, and a nonconvex problem with several sets is reduced to a conveX problem with two sets in the product space, where it is solved via an alternating projection method. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: December 7, 2019

2002 conference paper

Hard-constrained signal feasibility problems

1997 IEEE International Conference on Acoustics, Speech, and Signal Processing. Presented at the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, Munich, Germany.

By: P. Combettes* & P. Bondon*

Event: 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing at Munich, Germany on April 21-24, 1997

TL;DR: This work first investigates the process of aggregating soft constraints in order to define relevant objectives and then addresses the question of solving the resulting convex programs. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: December 7, 2019

2002 conference paper

Nonlinear multiresolution image analysis via convex projections

Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269), 2, 762–765.

By: P. Combettes & J. Pesquet*

Event: IPCIP'98 International Conference on Image Processing at Chicago, Illinois on October 7, 1998

TL;DR: A nonlinear extension of this framework in which the vector subspaces are replaced by convex subsets is proposed in order to provide a recursive, monotone approximation scheme that allows for various image features to be investigated. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: September 8, 2020

2002 conference paper

Operator theoretic image coding

1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings. Presented at the 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings, Atlanta, Georgia.

By: H. Puh* & P. Combettes*

Event: 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings at Atlanta, Georgia on May 9, 1996

TL;DR: The proposed formalism provides a flexible treatment of the image coding problem and contains as special cases transform coding, fractal coding, set theoretic coding, and vector quantization. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: December 7, 2019

2002 journal article

Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization

Journal of the Optical Society of America A, 19(7), 1334.

By: H. Bauschke*, P. Combettes* & D. Luke*

TL;DR: A theoretical framework is provided to better understand and to improve existing phase recovery algorithms and to establish new connections between well-established numerical phase retrieval schemes and classical convex optimization methods. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 18, 2019

2001 journal article

A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces

Mathematics of Operations Research, 26(2), 248–264.

By: H. Bauschke* & P. Combettes*

author keywords: convex feasibility; Fejer-monotonicity; firmly nonexpansive mapping; fixed point; Haugazeau; maximal monotone operator; projection; proximal point algorithm; resolvent; subgradient algorithm
TL;DR: A simple modification of iterative methods arising in numerical mathematics and optimization that makes them strongly convergent without additional assumptions is presented. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 18, 2019

2001 conference paper

Convexité et signal

Actes du Congrès de Mathématiques Appliquées et Industrielles SMAI'01, 6–16.

By: P. Combettes

Event: Actes du Congrès de Mathématiques Appliquées et Industrielles SMAI'01 at Pompadour, France on May 28 - June 1, 2001

Source: NC State University Libraries
Added: November 10, 2021

2001 journal article

Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces

Communications in Contemporary Mathematics, 3(4), 615–647.

By: H. Bauschke*, J. Borwein* & P. Combettes*

author keywords: Bregman distance; Bregman projection; coercive; cofinite function; convex function of Legendre type; essentially smooth; essentially strictly convex; Legendre function; Schur property; Schur space; subdifferential; supercoercive; weak Asplund space; zone consistent
Sources: Crossref, NC State University Libraries
Added: September 18, 2019

2001 chapter

Fejér-monotonicity in convex optimization

In C. A. Floudas & P. M. Pardalos (Eds.), Encyclopedia of Optimization (Vol. 2, pp. 106–114). New York: Springer-Verlag.

By: P. Combettes

Ed(s): C. Floudas & P. Pardalos

Source: NC State University Libraries
Added: September 9, 2019

2001 journal article

On the numerical robustness of the parallel projection method in signal synthesis

IEEE Signal Processing Letters, 8(2), 45–47.

By: P. Combettes*

author keywords: convex constraint; numerical errors; parallel computing; projection; signal recovery; signal synthesis
TL;DR: It is shown that the convergence properties of PPM remain valid under a simple summability condition on the relaxed averages of the errors, suggesting that the signal that least violates constraints in an average squared-distance sense remains valid. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: August 18, 2019

2001 chapter

Quasi-Fejérian Analysis of Some Optimization Algorithms

In Studies in Computational Mathematics (pp. 115–152).

By: P. Combettes*

TL;DR: A quasi-Fejer sequence is a sequence which satisfies the standard Fejer monotonicityproperty to within an additional error term and is shown to provide a powerful framework to analyze the convergence of a wide range of optimization algorithms in a systematic fashion. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 18, 2019

2000 journal article

Strong Convergence of Block-Iterative Outer Approximation Methods for Convex Optimization

SIAM Journal on Control and Optimization, 38(2), 538–565.

By: P. Combettes*

author keywords: block-iterative; convex feasibility problem; convex programming; constrained minimization; cutting plane; fixed point; inconsistent constraints; outer approximation; projection onto an intersection of convex sets; reflexive Banach space; surrogate cut; uniformly convex function
TL;DR: The strong convergence of a broad class of outer approximation methods for minimizing a convex function over the intersection of an arbitrary number of convex sets in a reflexive Banach space is studied in a unified framework. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 18, 2019

1999 conference paper

A subgradient projection algorithm for nondifferentiable signal recovery

Proceedings of the IEEE Workshop on Nonlinear Signal and Image Processing, 452–456.

By: J. Luo & P. Combettes

Event: Proceedings of the IEEE Workshop on Nonlinear Signal and Image Processing at Antalya, Turkey on June 20-23, 1999

Source: NC State University Libraries
Added: September 8, 2020

1999 journal article

Hard-constrained inconsistent signal feasibility problems

IEEE Transactions on Signal Processing, 47(9), 2460–2468.

By: P. Combettes* & P. Bondon*

author keywords: convex feasibility problem; fixed point; Hilbert space; inconsistent constraints; monotone operator; optimization; signal synthesis
TL;DR: This work considers the problem of synthesizing feasible signals in a Hilbert space in the presence of inconsistent convex constraints, and proposes a formalism and algorithmic framework that unify and extend existing approaches to inconsistent signal feasibility problems. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 18, 2019

1998 conference paper

Constrained pulse shape synthesis for digital communications

Proceedings of the European Signal Processing Conference, 573–576.

By: P. Combettes & P. Bondon

Event: Proceedings of the European Signal Processing Conference at Island of Rhodes, Greece on September 8-11, 1998

Source: NC State University Libraries
Added: September 8, 2020

1998 journal article

Convex multiresolution analysis

IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(12), 1308–1318.

By: P. Combettes* & J. Pesquet*

author keywords: multiresolution analysis; convex sets; hierarchical signal analysis; nonlinear filter banks; projections
Sources: Crossref, NC State University Libraries
Added: August 18, 2019

1997 journal article

Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections

IEEE Transactions on Image Processing, 6(4), 493–506.

By: P. Combettes*

TL;DR: This work proposes a general parallel projection method (EMOPSP) that not only generalizes existing projection-based schemes, but it also converges very efficiently thanks to its extrapolated relaxations. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 18, 2019

1997 journal article

Hilbertian convex feasibility problem: Convergence of projection methods

Applied Mathematics & Optimization, 35(3), 311–330.

By: P. Combettes*

Sources: Crossref, NC State University Libraries
Added: August 18, 2019

1996 conference paper

Bounded-error models in inverse problems

Proceedings of the 1996 IMACS/IEEE MultiConference on Computational Engineering in Systems Applications, 2, 1023–1027.

By: P. Combettes

Event: Proceedings of the 1996 IMACS/IEEE MultiConference on Computational Engineering in Systems Applications at Lille, France on July 9-12, 1996

Source: NC State University Libraries
Added: September 8, 2020

1996 journal article

Combining statistical information in set theoretic estimation

IEEE Signal Processing Letters, 3(3), 61–62.

By: P. Combettes* & T. Chaussalet*

TL;DR: The reliability of the set theoretic estimates resulting from the combination of multiple statistical constraints has thus far not been investigated and is addressed in order to provide a basis for a better use of statistical information inSet theoretic estimation problems. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1996 conference paper

Set theoretic vector quantization

Proceedings of the Ninth IEEE Workshop on Image and Multidimensional Signal Processing, 48–49.

By: H. Puh & P. Combettes

Event: Proceedings of the Ninth IEEE Workshop on Image and Multidimensional Signal Processing at Belize City, Belize on March 3-6, 1996

Source: NC State University Libraries
Added: September 8, 2020

1996 chapter

The Convex Feasibility Problem in Image Recovery

In Advances in Imaging and Electron Physics (pp. 155–270).

By: P. Combettes*

Sources: Crossref, NC State University Libraries
Added: August 19, 2019

1996 journal article

Wavelet synthesis by alternating projections

IEEE Transactions on Signal Processing, 44(3), 728–732.

By: J. Pesquet* & P. Combettes*

TL;DR: An alternating projection method is proposed to solve the constrained optimization problem of the coefficients of the quadrature mirror filters involved in orthonormal wavelet or wavelet packets signal decompositions. (via Semantic Scholar)
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1995 conference paper

Adaptive linear filtering with convex constraints

1995 International Conference on Acoustics, Speech, and Signal Processing, 2, 1372–1375.

By: P. Combettes* & P. Bondon*

Event: 1995 International Conference on Acoustics, Speech, and Signal Processing at Detroit, Michigan on May 9-12, 1995

TL;DR: This work addresses the problem of linear mean-square estimation with arbitrary convex constraints for dependent processes and proposes two algorithms, which are deterministic and stochastic and adaptive, and their convergence is established. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 8, 2020

1995 conference paper

Constrained image recovery in a product space

Proceedings., International Conference on Image Processing, 2, 25–28.

By: P. Combettes*

Event: International Conference on Image Processing at Washington, DC on October 23-26, 1995

TL;DR: This paper presents a product space framework for solving image recovery problems, which leads to simplified formulations and to efficient parallel algorithms. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: September 8, 2020

1995 journal article

Construction d'un point fixe commun à une famille de contractions fermes

Comptes Rendus De l'Académie Des Sciences De Paris, Série I (Mathématique), 320(11), 1385–1390.

By: P. Combettes

Source: NC State University Libraries
Added: September 18, 2019

1995 journal article

Deconvolution with bounded uncertainty

International Journal of Adaptive Control and Signal Processing, 9(1), 3–17.

By: P. Combettes* & H. Trussell

author keywords: SIGNAL DECONVOLUTION; BOUNDED-ERROR; SET THEORETIC ESTIMATION; CONVEX SETS; PROJECTIONS
TL;DR: This paper develops an abstract set theoretic deconvolution framework for problems in which the only information available about sources of uncertainty consists of bounds, and Iterative methods based on projections are used to generate solutions consistent with these bounds, the output data signal and a priori knowledge about the input signal. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1995 chapter

Restauration ensembliste d’images par itérations parallèles extrapolées de sous-gradients

In Actes du Quinzième Colloque GRETSI (pp. 447–450). http://hdl.handle.net/2042/12207

By: P. Combettes

Event: Actes du Quinzième Colloque GRETSI at Juan-les-Pins, France on September 18-22, 1995

Source: NC State University Libraries
Added: September 8, 2020

1995 journal article

Volterra filtering and higher order whiteness

IEEE Transactions on Signal Processing, 43(9), 2209–2212.

By: P. Bondon*, P. Combettes* & B. Picinbono*

TL;DR: Finite-order, finite-horizon Volterra filtering is investigated as well as its asymptotic properties and generalizations of the notion of white noise to higher orders are introduced. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1994 conference paper

A fast parallel projection algorithm for set theoretic image recovery

Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing, 5, 473–476.

By: P. Combettes* & H. Puh*

Event: ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing at Adelaide, Australia on April 19-22, 1994

TL;DR: A new projection algorithm for convex set theoretic image recovery [reconstruction and restoration] is presented that outperforms existing ones, in particular the popular cyclic method of projections onto convex sets [POCS]. (via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 8, 2020

1994 conference paper

Convex set theoretic image recovery via chaotic iterations of approximate projections

Proceedings of 1st International Conference on Image Processing, 3, 182–186.

By: P. Combettes*

Event: 1st International Conference on Image Processing at Austin, Texas on November 13-16, 1994

TL;DR: A general parallel iterative method which processes chaotically approximate projections instead of exact ones is proposed and subgradient projection methods are discussed as a particular case. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: September 8, 2020

1994 journal article

Inconsistent signal feasibility problems: least-squares solutions in a product space

IEEE Transactions on Signal Processing, 42(11), 2955–2966.

By: P. Combettes*

TL;DR: Presents parallel projection methods to find least-squares solutions to inconsistent convex set theoretic signal synthesis problems and convergence properties of the proposed methods are analyzed and signal synthesis applications are demonstrated. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science)
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1994 journal article

Iterations of parallel convex projections in hilbert spaces

Numerical Functional Analysis and Optimization, 15(3-4), 225–243.

By: P. Combettes* & H. Puh*

Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1994 conference paper

Selecting Statistical Information In Set Theoretic Signal Processing

IEEE Seventh SP Workshop on Statistical Signal and Array Processing, 55–58.

By: P. Combettes* & T. Chaussalet*

Event: IEEE Seventh SP Workshop on Statistical Signal and Array Processing at Quebec City, Quebec, Canada on June 26-29, 1994

Sources: Crossref, NC State University Libraries
Added: September 8, 2020

1994 conference paper

Set Theoretic Signal Processing

IEEE Seventh SP Workshop on Statistical Signal and Array Processing, 1–6.

By: P. Combettes*

Event: IEEE Seventh SP Workshop on Statistical Signal and Array Processing at Quebec City, Quebec, Canada on June 26-29, 1994

Sources: Crossref, NC State University Libraries
Added: September 8, 2020

1994 conference paper

Synthèse ensembliste d’ondelettes

Actes de la Conférence Temps-Fréquence, Ondelettes et Multirésolution, 14.1–14.10.

By: J. Pesquet & P. Combettes

Event: Actes de la Conférence Temps-Fréquence, Ondelettes et Multirésolution at Lyon, France on March 9-11, 1994

Source: NC State University Libraries
Added: September 8, 2020

1993 conference paper

A simultaneous projection method for inconsistent signal and image feasibility problems

Proceedings of the Eighth IEEE Workshop on Image and Multidimensional Signal Processing, 32–33.

By: P. Combettes

Event: Proceedings of the Eighth IEEE Workshop on Image and Multidimensional Signal Processing at Cannes, France on September 8-10, 1993

Source: NC State University Libraries
Added: September 8, 2020

1993 chapter

Estimation en présence de modèles incertains: sélection de formulations ensemblistes

In Actes du Quatorzième Colloque GRETSI (pp. 205–208). http://hdl.handle.net/2042/12154

By: P. Combettes & T. Chaussalet

Event: Actes du Quatorzième Colloque GRETSI at Juan-les-Pins, France on September 13-16, 1993

Source: NC State University Libraries
Added: September 8, 2020

1993 conference paper

Parallel projection methods for set theoretic signal reconstruction and restoration

IEEE International Conference on Acoustics Speech and Signal Processing. Presented at the 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing, Minneapolis, Minnesota.

By: P. Combettes* & H. Puh*

Event: 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing at Minneapolis, Minnesota on April 27-30, 1993

TL;DR: A general method of parallel projections (MOPP) for solving feasibility problems in Hilbert spaces is proposed and MOPP is seen to have substantial advantages over the method of successive projections. (via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: January 5, 2020

1993 journal article

Signal recovery by best feasible approximation

IEEE Transactions on Image Processing, 2(2), 269–271.

By: P. Combettes*

TL;DR: Methods for projecting a point onto the intersection of closed and convex sets in a Hilbert space are introduced and applied to signal recovery by best feasible approximation of a reference signal. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1993 journal article

The foundations of set theoretic estimation

Proceedings of the IEEE, 81(2), 182–208.

By: P. Combettes*

UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science)
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1993 conference paper

Volterra prediction models and higher order whiteness

IEEE International Conference on Acoustics Speech and Signal Processing. Presented at the 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing, Minneapolis, Minnesota.

By: P. Bondon*, P. Combettes* & B. Picinbono*

Event: 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing at Minneapolis, Minnesota on April 27-30, 1993

TL;DR: The authors study Volterra predictors and compare them with their linear counterparts to show that a nonlinear predictor can achieve a smaller prediction error than a linear one. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 5, 2020

1992 journal article

A bound for the zeros of polynomials

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 39(6), 476–478.

By: M. Zilovic*, L. Roytman*, P. Combettes* & M. Swamy*

Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1992 conference paper

A general framework for the incorporation of uncertainty in set theoretic estimation

ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing. Presented at the ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, San Francisco, California.

By: P. Combettes*, M. Benidir* & B. Picinbono*

Event: ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing at San Francisco, California on March 23-26, 1992

TL;DR: A general framework is developed to construct sets in the solution space by constraining the estimation residual based on the known component of the model to be consistent with those known properties of a so-called uncertainty process. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 5, 2020

1992 journal article

Best stable and invertible approximations for ARMA systems

IEEE Transactions on Signal Processing, 40(12), 3066–3069.

By: P. Combettes* & H. Trussell n

TL;DR: A method is proposed for finding the best stable and invertible approximations for an autoregressive moving average (ARMA) system, relative to a general quadratic metric in the coefficient space, by constrained steepest descent in the hypercube of reflection coefficients. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1992 journal article

Convex set theoretic image recovery: History, current status, and new directions

Journal of Visual Communication and Image Representation, 3(4), 307–315.

By: P. Combettes*

TL;DR: A historical overview of convex set theoretic image recovery is given, its most significant developments are surveyed, its current limitations are analyzed, and new directions for theoretical and applied research are proposed. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1992 conference paper

Large dimensional random matrix theory for signal detection and estimation in array processing

IEEE Sixth SP Workshop on Statistical Signal and Array Processing, 276–279.

By: J. Silverstein n & P. Combettes*

Event: IEEE Sixth SP Workshop on Statistical Signal and Array Processing at Victoria, British Columbia, Canada on October 7-9, 1992

Sources: Crossref, NC State University Libraries
Added: August 25, 2020

1992 journal article

Signal detection via spectral theory of large dimensional random matrices

IEEE Transactions on Signal Processing, 40(8), 2100–2105.

By: J. Silverstein n & P. Combettes*

TL;DR: The theoretical analysis presented focuses on the splitting of the spectrum of sample covariance matrix into noise and signal eigenvalues and it is shown that when the number of sensors is large thenumber of signals can be estimated with a sample size considerably less than that required by previous approaches. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1992 conference paper

What is a good estimate?

Proceedings of the European Signal Processing Conference, 713–716.

By: P. Combettes & W. Edmonson

Event: Proceedings of the European Signal Processing Conference at Brussels, Belgium on August 24-27, 1992

Source: NC State University Libraries
Added: September 8, 2020

1991 conference paper

Critères de qualité en estimation ensembliste

Actes du Treizième Colloque GRETSI, 249–252. Juan-les-Pins.

By: P. Combettes & T. Chaussalet

Event: Actes du Treizième Colloque GRETSI at Juan-les-Pins, France on September 16-20, 1991

Source: NC State University Libraries
Added: September 8, 2020

1991 journal article

Set theoretic estimation by random search

IEEE Transactions on Signal Processing, 39(7), 1669–1671.

By: P. Combettes* & H. Trussell n

TL;DR: An adapted random search algorithm is shown to be a feasible method for the synthesis of set theoretic estimates and can handle arbitrarily complex property sets in applications for which the number of unknown parameters is typically low. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1991 conference paper

The foundations of set theoretic estimation

[Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing. Presented at the ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing, Toronto, Ontario, Canada.

By: P. Combettes* & M. Civanlar*

Event: ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing at Toronto, Ontario, Canada on April 14-17, 1991

TL;DR: A single formal framework is presented to synthesize various approaches to set theory estimation, and the fundamental philosophy, goals, and analytical techniques of set theoretic estimation are discussed. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 5, 2020

1991 journal article

The use of noise properties in set theoretic estimation

IEEE Transactions on Signal Processing, 39(7), 1630–1641.

By: P. Combettes* & H. Trussell n

TL;DR: The authors describe how a wide range of Probabilistic information pertaining to the noise process can be used in a general set theoretic estimation framework to constrain the sample statistics of the estimation residual to be consistent with those probabilistic properties of the noise which are available and to construct sets accordingly in the solution space. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1990 journal article

Method of successive projections for finding a common point of sets in metric spaces

Journal of Optimization Theory and Applications, 67(3), 487–507.

By: P. Combettes* & H. Trussell n

author keywords: SUCCESSIVE PROJECTIONS; CONVERGENCE; NONLINEAR OPTIMIZATION; SET-VALUED PROJECTIONS; METRIC SPACES
UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science)
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1990 conference paper

New methods for the synthesis of set theoretic estimates (digital signal processing)

International Conference on Acoustics, Speech, and Signal Processing, 2531–2534.

By: P. Combettes n & H. Trussell n

Event: International Conference on Acoustics, Speech, and Signal Processing at Albuquerque, New Mexico on April 3-6, 1990

TL;DR: Two methods for the synthesis of set theoretic estimates are presented, including a generalization of the method of successive projections onto closed and convex subsets of Hilbert spaces to approximately compact subset of metric spaces based on a stochastic search in the solution space. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: September 8, 2020

1990 conference paper

Set theoretic autoregressive spectral estimation

Fifth ASSP Workshop on Spectrum Estimation and Modeling. Presented at the Fifth ASSP Workshop on Spectrum Estimation and Modeling, Rochester, New York.

By: P. Combettes* & H. Trussell n

Event: Fifth ASSP Workshop on Spectrum Estimation and Modeling at Rochester, New York on October 10-12, 1990

TL;DR: The set theoretic approach in autoregressive (AR) spectral estimation is presented, which produces an estimate of the regression vector which has the property of being consistent with all the available a priori knowledge. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: January 5, 2020

1989 conference paper

General order moments in set theoretic estimation

International Conference on Acoustics, Speech, and Signal Processing, 2531–2534.

By: P. Combettes n & H. Trussell n

Event: International Conference on Acoustics, Speech, and Signal Processing at Glasgow, Scotland on May 23-26, 1989

TL;DR: A description is given of how information pertaining to an arbitrary absolute moment of the noise process can be used in a general set-theoretic estimation framework and it is shown that for each such piece of a priori information a set can be constructed in the solution space by constraining the corresponding sample statistics of the estimation residual to lie within some acceptable distance from the expected value. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: September 8, 2020

1989 journal article

Methods for digital restoration of signals degraded by a stochastic impulse response

IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(3), 393–401.

By: P. Combettes n & H. Trussell n

TL;DR: It is shown that the integration of the additional uncertainties caused by the variations of the impulse response of the stochastic degradation can be used to obtain better estimates. (via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: August 29, 2019

1988 conference paper

Stability of the linear prediction filter: a set theoretic approach

ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing, 2288–2291.

By: P. Combettes n & H. Trussell n

Event: ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing at New York, NY on April 11-14, 1988

TL;DR: The authors investigate the application of set-theoretic estimation methods to the design of linear-predictive-coding digital filters and identify the set of filters which minimize the mean-square prediction error in an environment where the statistics of the observed data are unknown. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: September 8, 2020

1987 conference paper

Considerations for the restoration of stochastic degradations

ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing, 1209–1212.

By: H. Trussell n & P. Combettes n

Event: IEEE International Conference on Acoustics, Speech, and Signal Processing at Dallas, Texas on April 6-9, 1987

TL;DR: It will be shown that the integration of the additional uncertainties caused by the stochastic psf can be used to obtain better estimates and can be included to the restoration scheme in a very flexible manner through the use of the Projection Onto Convex Sets (POCS) method. (via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Crossref, NC State University Libraries
Added: September 8, 2020

1987 conference paper

Modèles et algorithmes en vue de la restauration numérique d’images rayons-X

Actes du Colloque MARI-Cognitiva Electronic Image, 146–151.

By: P. Combettes & H. Trussell

Event: Actes du Colloque MARI-Cognitiva Electronic Image at Paris, France on May 18-22, 1987

Source: NC State University Libraries
Added: September 8, 2020

Employment

Updated: August 29th, 2019 22:07

North Carolina State University Raleigh, NC, US
Distinguished Professor Mathematics

Citation Index includes data from a number of different sources. If you have questions about the sources of data in the Citation Index or need a set of data which is free to re-distribute, please contact us.

Certain data included herein are derived from the Web of Science© and InCites© (2024) of Clarivate Analytics. All rights reserved. You may not copy or re-distribute this material in whole or in part without the prior written consent of Clarivate Analytics.