Patrick Louis Combettes

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

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

BLOCK-ACTIVATED ALGORITHMS FOR MULTICOMPONENT FULLY NONSMOOTH MINIMIZATION

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

SIGNAL RECOVERY FROM INCONSISTENT NONLINEAR OBSERVATIONS

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

A Fixed Point Framework for Recovering Signals from Nonlinear Transformations

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

Analysis and numerical solution of a modular convex Nash equilibrium problem

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

Block-activated algorithms for multicomponent fully nonsmooth minimization

(ArXiv Preprint No. 2103.00520). https://arxiv.org/abs/2103.00520

Bregman Forward-Backward Operator Splitting

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

Fixed Point Strategies in Data Science

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

Multivariate Monotone Inclusions in Saddle Form

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

Reconstruction of functions from prescribed proximal points

Journal of Approximation Theory, 268, 105606.

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

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

Solving Composite Fixed Point Problems with Block Updates

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

Deep Neural Network Structures Solving Variational Inequalities

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

Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operators

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

Perspective maximum likelihood-type estimation via proximal decomposition

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

The Douglas--Rachford Algorithm Converges Only Weakly

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

Warped proximal iterations for monotone inclusions

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

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.

Learning with optimal interpolation norms

Numerical Algorithms, 81(2), 695–717.

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

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

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

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

Consistent learning by composite proximal thresholding

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

Linear convergence of stochastic block-coordinate fixed point algorithms

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

Monotone operator theory in convex optimization

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

Perspective Functions: Properties, Constructions, and Examples

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

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

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

Regularized learning schemes in feature Banach spaces

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

Classification and Regression Using an Outer Approximation Projection-Gradient Method

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

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

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

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.

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

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

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.

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

Pure and Applied Functional Analysis, 1(1), 13–37.

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.

A strongly convergent primal–dual method for nonoverlapping domain decomposition

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

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

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

Compositions and convex combinations of averaged nonexpansive operators

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

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.

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

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

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

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

A primal-dual method of partial inverses for composite inclusions

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

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.

Asymptotic behavior of compositions of under-relaxed nonexpansive operators

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

Modern convex analysis

Mathematical Programming, 148, 1–4.

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

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

Monotone Operator Methods for Nash Equilibria in Non-potential Games

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

Moreau’s decomposition in Banach spaces

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

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

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

Variable metric quasi-Fejér monotonicity

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

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

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

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

Optimization, 63(9), 1289–1318.

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

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

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

In CMS Books in Mathematics.

Fixed-Point Algorithms for Inverse Problems in Science and Engineering

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

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

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.

Proximal Splitting Methods in Signal Processing

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

Proximity for sums of composite functions

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

A Parallel Splitting Method for Coupled Monotone Inclusions

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

Alternating proximal algorithm for blind image recovery

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

Dualization of Signal Recovery Problems

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

Functions with prescribed best linear approximations

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

Proximal Algorithms for Multicomponent Image Recovery Problems

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

Proximal method for geometry and texture image decomposition

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

The Baillon-Haddad theorem revisited

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

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

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

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

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

Split convex minimization algorithm for signal recovery

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

A Convex Programming Algorithm for Noisy Discrete Tomography

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

A Dykstra-like algorithm for two monotone operators

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

A proximal decomposition method for solving convex variational inverse problems

Inverse Problems, 24(6), 065014.

Proximal Thresholding Algorithm for Minimization over Orthonormal Bases

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

Visco-penalization of the sum of two monotone operators

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

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

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

A variational formulation for frame-based inverse problems

Inverse Problems, 23(4), 1495–1518.

Opérateurs proximaux pour la restauration bayésienne de signaux

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

Sparse signal recovery by iterative proximal thresholding

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

A decomposition method for nonsmooth convex variational signal recovery

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

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.

Approximating curves for nonexpansive and monotone operators

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

Iterative image deconvolution using overcomplete representations

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

Joint minimization with alternating Bregman proximity operators

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

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.

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.

Equilibrium programming in Hilbert spaces

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

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.

Extrapolation algorithm for affine-convex feasibility problems

Numerical Algorithms, 41(3), 239–274.

Parallel Block-Iterative Reconstruction Algorithms for Binary Tomography

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

Signal Recovery by Proximal Forward-Backward Splitting

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

The asymptotic behavior of the composition of two resolvents

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

The asymptotic behavior of the composition of two resolvents

Nonlinear Analysis, 60(2), 283–301.

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.

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.

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.

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

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

Image Restoration Subject to a Total Variation Constraint

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

Proximal Methods for Cohypomonotone Operators

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

Solving monotone inclusions via compositions of nonexpansive averaged operators

Optimization, 53(5-6), 475–504.

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.

Wavelet-constrained image restoration

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

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

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

Bregman Monotone Optimization Algorithms

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

Construction of best Bregman approximations in reflexive Banach spaces

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

Hybrid projection–reflection method for phase retrieval

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

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.

Iterating Bregman Retractions

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

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.

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.

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.

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.

An adaptive level set method for nondifferentiable constrained image recovery

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

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.

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.

Generalized Mann iterates for constructing fixed points in Hilbert spaces

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

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.

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.

Nonlinear multiresolution image analysis via convex projections

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

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.

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

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

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

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

Convexité et signal

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

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

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

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.

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

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

Quasi-Fejérian Analysis of Some Optimization Algorithms

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

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

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

A subgradient projection algorithm for nondifferentiable signal recovery

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

Hard-constrained inconsistent signal feasibility problems

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

Constrained pulse shape synthesis for digital communications

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

Convex multiresolution analysis

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

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

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

Hilbertian convex feasibility problem: Convergence of projection methods

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

Bounded-error models in inverse problems

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

Combining statistical information in set theoretic estimation

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

Set theoretic vector quantization

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

The Convex Feasibility Problem in Image Recovery

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

Wavelet synthesis by alternating projections

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

Adaptive linear filtering with convex constraints

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

Constrained image recovery in a product space

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

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.

Deconvolution with bounded uncertainty

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

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

Volterra filtering and higher order whiteness

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

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.

Convex set theoretic image recovery via chaotic iterations of approximate projections

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

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

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