Patrick Combettes

Briceno-Arias, L. M., Combettes, P. L., & Silva, F. J. (2024, February 19). Perspective functions with nonlinear scaling. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, Vol. 2. https://doi.org/10.1142/S0219199723500657

The geometry of monotone operator  splitting methods (to appear, available on arxiv). (2024). Acta Numerica.

Briceno-Arias, L. M., & Combettes, P. L. (2023, October 17). A Perturbation Framework for Convex Minimization and Monotone Inclusion Problems with Nonlinear Compositions. MATHEMATICS OF OPERATIONS RESEARCH, Vol. 10. https://doi.org/10.1287/moor.2022.0180

Combettes, P. L. (2023). Resolvent and Proximal Compositions. SET-VALUED AND VARIATIONAL ANALYSIS, 31(3). https://doi.org/10.1007/s11228-023-00678-z

Combettes, P. L., & Woodstock, Z. C. (2022). A Variational Inequality Model for the Construction of Signals from Inconsistent Nonlinear Equations\ast. SIAM JOURNAL ON IMAGING SCIENCES, 15(1), 84–109. https://doi.org/10.1137/21M1420368

Bui, M. N., Combettes, P. L., & Woodstock, Z. C. (2022). BLOCK-ACTIVATED ALGORITHMS FOR MULTICOMPONENT FULLY NONSMOOTH MINIMIZATION. 2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), pp. 5428–5432. https://doi.org/10.1109/ICASSP43922.2022.9747479

Combettes, P. L., & Woodstock, Z. C. (2022). SIGNAL RECOVERY FROM INCONSISTENT NONLINEAR OBSERVATIONS. 2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), pp. 5872–5876. https://doi.org/10.1109/ICASSP43922.2022.9746145

Combettes, P. L., & Woodstock, Z. C. (2021). A Fixed Point Framework for Recovering Signals from Nonlinear Transformations. 2020 28th European Signal Processing Conference (EUSIPCO), 2120–2124. https://doi.org/10.23919/eusipco47968.2020.9287736

Bùi, M. N., & Combettes, P. L. (2021). Analysis and numerical solution of a modular convex Nash equilibrium problem (HAL Preprint No. hal-03412172). Retrieved from https://hal.archives-ouvertes.fr/hal-03412172

Bùi, M. N., Combettes, P. L., & Woodstock, Z. C. (2021). Block-Activated Algorithms for Multicomponent Fully Nonsmooth Minimization (ArXiv Preprint No. 2103.00520). https://doi.org/10.48550/arXiv.2103.00520

Bui, M. N., & Combettes, P. L. (2021). Bregman Forward-Backward Operator Splitting. Set-Valued and Variational Analysis, 29(3), 583–603. https://doi.org/10.1007/s11228-020-00563-z

Combettes, P. L., & Pesquet, J.-C. (2021). Fixed Point Strategies in Data Science. IEEE Transactions on Signal Processing, 69, 3878–3905. https://doi.org/10.1109/TSP.2021.3069677

Bui, M. N., & Combettes, P. L. (2021, December 21). Multivariate Monotone Inclusions in Saddle Form. MATHEMATICS OF OPERATIONS RESEARCH, Vol. 12. https://doi.org/10.1287/moor.2021.1161

Combettes, P. L., & Woodstock, Z. C. (2021). Reconstruction of functions from prescribed proximal points. Journal of Approximation Theory, 268, 105606. https://doi.org/10.1016/j.jat.2021.105606

Combettes, P. L., & Mueller, C. L. (2021). Regression Models for Compositional Data: General Log-Contrast Formulations, Proximal Optimization, and Microbiome Data Applications. Statistics in Biosciences, 13(2), 217–242. https://doi.org/10.1007/s12561-020-09283-2

Combettes, P. L., & Glaudin, L. E. (2021). Solving Composite Fixed Point Problems with Block Updates. Advances in Nonlinear Analysis, 10(1), 1154–1177. https://doi.org/10.1515/anona-2020-0173

Combettes, P. L., & Pesquet, J.-C. (2020). Deep Neural Network Structures Solving Variational Inequalities. Set-Valued and Variational Analysis, 28(3), 491–518. https://doi.org/10.1007/s11228-019-00526-z

Combettes, P. L., & Pesquet, J.-C. (2020). Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operators. SIAM Journal on Mathematics of Data Science, 2(2), 529–557. https://doi.org/10.1137/19m1272780

Combettes, P. L., & Müller, C. L. (2020). Perspective maximum likelihood-type estimation via proximal decomposition. Electronic Journal of Statistics, 14(1), 207–238. https://doi.org/10.1214/19-EJS1662

Bùi, M. N., & Combettes, P. L. (2020). The Douglas--Rachford Algorithm Converges Only Weakly. SIAM Journal on Control and Optimization, 58(2), 1118–1120. https://doi.org/10.1137/19M1308451

Bùi, M. N., & Combettes, P. L. (2020). Warped proximal iterations for monotone inclusions. Journal of Mathematical Analysis and Applications, 491(1), 124315. https://doi.org/10.1016/j.jmaa.2020.124315

Combettes, P. L., & Glaudin, L. E. (2019). 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. https://doi.org/10.23919/eusipco.2019.8903039

Combettes, P. L., McDonald, A. M., Micchelli, C. A., & Pontil, M. (2019). Learning with optimal interpolation norms. Numerical Algorithms, 81(2), 695–717. https://doi.org/10.1007/s11075-018-0568-1

Combettes, P. L., & Glaudin, L. E. (2019). Proximal Activation of Smooth Functions in Splitting Algorithms for Convex Image Recovery. SIAM Journal on Imaging Sciences, 12(4), 1905–1935. https://doi.org/10.1137/18M1224763

Combettes, P. L., & Pesquet, J.-C. (2019). Stochastic quasi-Fejer block-coordinate fixed point iterations with random sweeping II: mean-square and linear convergence. Mathematical Programming, 174(1-2), 433–451. https://doi.org/10.1007/s10107-018-1296-y

Combettes, P. L., Salzo, S., & Villa, S. (2018). Consistent learning by composite proximal thresholding. MATHEMATICAL PROGRAMMING, 167(1), 99–127. https://doi.org/10.1007/s10107-017-1133-8

Combettes, P. L., & Pesquet, J.-C. (2018). Linear convergence of stochastic block-coordinate fixed point algorithms. Proceedings of the European Signal Processing Conference, 747–751. https://doi.org/10.23919/EUSIPCO.2018.8552941

Combettes, P. L. (2018, July). Monotone operator theory in convex optimization. MATHEMATICAL PROGRAMMING, Vol. 170, pp. 177–206. https://doi.org/10.1007/s10107-018-1303-3

Combettes, P. L. (2018). Perspective Functions: Properties, Constructions, and Examples. SET-VALUED AND VARIATIONAL ANALYSIS, 26(2), 247–264. https://doi.org/10.1007/s11228-017-0407-x

Combettes, P. L., & Muller, C. L. (2018). Perspective functions: Proximal calculus and applications in high-dimensional statistics. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 457(2), 1283–1306. https://doi.org/10.1016/j.jmaa.2016.12.021

Combettes, P. L., Salzo, S., & Villa, S. (2018). Regularized learning schemes in feature Banach spaces. ANALYSIS AND APPLICATIONS, 16(1), 1–54. https://doi.org/10.1142/s0219530516500202

Barlaud, M., Belhajali, W., Combettes, P. L., & Fillatre, L. (2017). Classification and Regression Using an Outer Approximation Projection-Gradient Method. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 65(17), 4635–4644. https://doi.org/10.1109/tsp.2017.2709262

Bauschke, H. H., & Combettes, P. L. (2017). Convex Analysis and Monotone Operator Theory in Hilbert Spaces. In CMS Books in Mathematics (2nd ed.). https://doi.org/10.1007/978-3-319-48311-5

Combettes, P. L., & Glaudin, L. E. (2017). 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. https://doi.org/10.1137/17m112806x

Combettes, P. L., & Eckstein, J. (2016). Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions. Mathematical Programming, 168(1-2), 645–672. https://doi.org/10.1007/s10107-016-1044-0

Combettes, P. L., & Nguyen, Q. V. (2016). 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.

Combettes, P. L., & Pesquet, J.-C. (2016). Stochastic approximations and perturbations in forward-backward splitting for monotone operators. Pure and Applied Functional Analysis, 1(1), 13–37. Retrieved from http://www.yokohamapublishers.jp/online2/oppafa/vol1/p13.html

Combettes, P. L., & Pesquet, J.-C. (2016). 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. https://doi.org/10.1109/EUSIPCO.2016.7760561

Attouch, H., Briceño-Arias, L. M., & Combettes, P. L. (2015). A strongly convergent primal–dual method for nonoverlapping domain decomposition. Numerische Mathematik, 133(3), 443–470. https://doi.org/10.1007/s00211-015-0751-4

Alotaibi, A., Combettes, P. L., & Shahzad, N. (2015). Best Approximation from the Kuhn-Tucker Set of Composite Monotone Inclusions. Numerical Functional Analysis and Optimization, 36(12), 1513–1532. https://doi.org/10.1080/01630563.2015.1077864

Combettes, P. L., & Yamada, I. (2015). Compositions and convex combinations of averaged nonexpansive operators. Journal of Mathematical Analysis and Applications, 425(1), 55–70. https://doi.org/10.1016/j.jmaa.2014.11.044

Combettes, P. L., & Dũng, D. (2015). 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. https://doi.org/10.1007/s11228-015-0338-3

Combettes, P. L., & Pesquet, J.-C. (2015). Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping. SIAM Journal on Optimization, 25(2), 1221–1248. https://doi.org/10.1137/140971233

Combettes, P. L., Condat, L., Pesquet, J.-C., & Vũ, B. C. (2014). A forward-backward view of some primal-dual optimization methods in image recovery. Proceedings of the IEEE International Conference on Image Processing, 4141–4145. https://doi.org/10.1109/ICIP.2014.7025841

Alghamdi, M. A., Alotaibi, A., Combettes, P. L., & Shahzad, N. (2014). A primal-dual method of partial inverses for composite inclusions. Optimization Letters, 8(8), 2271–2284. https://doi.org/10.1007/s11590-014-0734-x

Becker, S. R., & Combettes, P. L. (2014). 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.

Baillon, J.-B., Combettes, P. L., & Cominetti, R. (2014). Asymptotic behavior of compositions of under-relaxed nonexpansive operators. Journal of Dynamics and Games, 1(3), 331–346. https://doi.org/10.3934/jdg.2014.1.331

Combettes, P. L., Hiriart-Urruty, J.-B., & Théra, M. (2014). Modern convex analysis. Mathematical Programming, 148, 1–4. https://doi.org/10.1007/s10107-014-0815-8

Alotaibi, A., Combettes, P. L., & Shahzad, N. (2014). Solving Coupled Composite Monotone Inclusions by Successive Fejér Approximations of their Kuhn--Tucker Set. SIAM Journal on Optimization, 24(4), 2076–2095. https://doi.org/10.1137/130950616

Briceño-Arias, L. M., & Combettes, P. L. (2013). Monotone Operator Methods for Nash Equilibria in Non-potential Games. In Computational and Analytical Mathematics (pp. 143–159). https://doi.org/10.1007/978-1-4614-7621-4_9

Combettes, P. L., & Reyes, N. N. (2013). Moreau’s decomposition in Banach spaces. Mathematical Programming, 139(1-2), 103–114. https://doi.org/10.1007/s10107-013-0663-y

Combettes, P. L. (2013). Systems of Structured Monotone Inclusions: Duality, Algorithms, and Applications. SIAM Journal on Optimization, 23(4), 2420–2447. https://doi.org/10.1137/130904160

Combettes, P. L., & Vũ, B. C. (2013). Variable metric quasi-Fejér monotonicity. Nonlinear Analysis: Theory, Methods & Applications, 78, 17–31. https://doi.org/10.1016/j.na.2012.09.008

Baillon, J.-B., Combettes, P. L., & Cominetti, R. (2012). There is no variational characterization of the cycles in the method of periodic projections. Journal of Functional Analysis, 262(1), 400–408. https://doi.org/10.1016/j.jfa.2011.09.002

Combettes, P. L., & Vũ, B. C. (2012). Variable metric forward–backward splitting with applications to monotone inclusions in duality. Optimization, 63(9), 1289–1318. https://doi.org/10.1080/02331934.2012.733883

Briceño-Arias, L. M., & Combettes, P. L. (2011). A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality. SIAM Journal on Optimization, 21(4), 1230–1250. https://doi.org/10.1137/10081602x

Bauschke, H. H., & Combettes, P. L. (2011). Convex Analysis and Monotone Operator Theory in Hilbert Spaces. In CMS Books in Mathematics. https://doi.org/10.1007/978-1-4419-9467-7

Bauschke, H. H., Burachik, R. S., Combettes, P. L., Elser, V., Luke, D. R., & Wolkowicz, H. (Eds.). (2011). Fixed-Point Algorithms for Inverse Problems in Science and Engineering. https://doi.org/10.1007/978-1-4419-9569-8

Censor, Y., Chen, W., Combettes, P. L., Davidi, R., & Herman, G. T. (2011). On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints. Computational Optimization and Applications, 51(3), 1065–1088. https://doi.org/10.1007/s10589-011-9401-7

Combettes, P. L., & Pesquet, J.-C. (2011). 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. https://doi.org/10.1007/s11228-011-0191-y

Combettes, P. L., & Pesquet, J.-C. (2011). Proximal Splitting Methods in Signal Processing. In Springer Optimization and Its Applications (pp. 185–212). https://doi.org/10.1007/978-1-4419-9569-8_10

Combettes, P. L., Dũng, Đ., & Vũ, B. C. (2011). Proximity for sums of composite functions. Journal of Mathematical Analysis and Applications, 380(2), 680–688. https://doi.org/10.1016/j.jmaa.2011.02.079

Attouch, H., Briceño-Arias, L. M., & Combettes, P. L. (2010). A Parallel Splitting Method for Coupled Monotone Inclusions. SIAM Journal on Control and Optimization, 48(5), 3246–3270. https://doi.org/10.1137/090754297

Bolte, J., Combettes, P. L., & Pesquet, J.-C. (2010). Alternating proximal algorithm for blind image recovery. Proceedings of the IEEE International Conference on Image Processing, 1673–1676. https://doi.org/10.1109/ICIP.2010.5652173

Combettes, P. L., Dũng, Đ., & Vũ Bằng Công. (2010). Dualization of Signal Recovery Problems. Set-Valued and Variational Analysis, 18(3-4), 373–404. https://doi.org/10.1007/s11228-010-0147-7

Combettes, P. L., & Reyes, N. N. (2010). Functions with prescribed best linear approximations. Journal of Approximation Theory, 162(5), 1095–1116. https://doi.org/10.1016/j.jat.2009.12.007

Briceño-Arias, L. M., Combettes, P. L., Pesquet, J.-C., & Pustelnik, N. (2010). Proximal Algorithms for Multicomponent Image Recovery Problems. Journal of Mathematical Imaging and Vision, 41(1-2), 3–22. https://doi.org/10.1007/s10851-010-0243-1

Briceño-Arias, L. M., Combettes, P. L., Pesquet, J.-C., & Pustelnik, N. (2010). Proximal method for geometry and texture image decomposition. Proceedings of the IEEE International Conference on Image Processing, 2721–2724. https://doi.org/10.1109/ICIP.2010.5653670

Bauschke, H. H., & Combettes, P. L. (2010). The Baillon-Haddad theorem revisited. Journal of Convex Analysis, 17(4), 781–787.

Briceño-Arias, L. M., & Combettes, P. L. (2009). Convex variational formulation with smooth coupling for multicomponent signal decomposition and recovery. Numerical Mathematics: Theory, Methods, and Applications, 2(4), 485–508. https://doi.org/10.4208/nmtma.2009.m9009s

Combettes, P. L. (2009). Iterative construction of the resolvent of a sum of maximal monotone operators. Journal of Convex Analysis, 16(4), 727–748.

Combettes, P. L., & Pesquet, J.-C. (2009). Split convex minimization algorithm for signal recovery. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 685–688. https://doi.org/10.1109/ICASSP.2009.4959676

Capricelli, T. D., & Combettes, P. L. (2008). A Convex Programming Algorithm for Noisy Discrete Tomography. In Advances in Discrete Tomography and Its Applications (pp. 207–226). https://doi.org/10.1007/978-0-8176-4543-4_10

Bauschke, H. H., & Combettes, P. L. (2008). A Dykstra-like algorithm for two monotone operators. Pacific Journal of Optimization, 4(3), 383–391.

Combettes, P. L., & Pesquet, J.-C. (2008). A proximal decomposition method for solving convex variational inverse problems. Inverse Problems, 24(6), 065014. https://doi.org/10.1088/0266-5611/24/6/065014

Combettes, P. L., & Pesquet, J.-C. (2008). Proximal Thresholding Algorithm for Minimization over Orthonormal Bases. SIAM Journal on Optimization, 18(4), 1351–1376. https://doi.org/10.1137/060669498

Combettes, P. L., & Hirstoaga, S. A. (2008). Visco-penalization of the sum of two monotone operators. Nonlinear Analysis: Theory, Methods & Applications, 69(2), 579–591. https://doi.org/10.1016/j.na.2007.06.003

Combettes, P. L., & Pesquet, J.-C. (2007). A Douglas–Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery. IEEE Journal of Selected Topics in Signal Processing, 1(4), 564–574. https://doi.org/10.1109/jstsp.2007.910264

Chaux, C., Combettes, P. L., Pesquet, J.-C., & Wajs, V. R. (2007). A variational formulation for frame-based inverse problems. Inverse Problems, 23(4), 1495–1518. https://doi.org/10.1088/0266-5611/23/4/008

Chaux, C., Combettes, P. L., Pesquet, J.-C., & Wajs, V. R. (2007). Opérateurs proximaux pour la restauration bayésienne de signaux. Proceedings of the Twenty First GRETSI Symposium, 1277–1280. Retrieved from http://hdl.handle.net/2042/17744

Combettes, P. L., & Pesquet, J.-C. (2007). Sparse signal recovery by iterative proximal thresholding. Proceedings of the European Signal Processing Conference. Presented at the European Signal Processing Conference, Poznan, Poland.

Bauschke, H. H., Combettes, P. L., & Pesquet, J.-C. (2006). A decomposition method for nonsmooth convex variational signal recovery. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 5, 989–992. https://doi.org/10.1109/ICASSP.2006.1661444

Bauschke, H. H., Combettes, P. L., & Luke, D. R. (2006). 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. https://doi.org/10.1016/j.jat.2006.01.003

Combettes, P. L., & Hirstoaga, S. A. (2006). Approximating curves for nonexpansive and monotone operators. Journal of Convex Analysis, 13(3-4), 633–646.

Chaux, C., Combettes, P. L., Pesquet, J. C., & Wajs, V. R. (2006). Iterative image deconvolution using overcomplete representations. Proceedings of the European Signal Processing Conference. Presented at the 14th European Signal Processing Conference, Florence, Italy.

Bauschke, H. H., Combettes, P. L., & Noll, D. (2006). Joint minimization with alternating Bregman proximity operators. Pacific Journal of Optimization, 2(3), 401–424.

Chaux, C., Combettes, P. L., Pesquet, J.-C., & Wajs, V. R. (2005). 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.

Bauschke, H. H., Combettes, P. L., & Luke, D. R. (2005). 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. https://doi.org/10.1109/ICASSP.2005.1415952

Combettes, P. L., & Hirstoaga, S. A. (2005). Equilibrium programming in Hilbert spaces. Journal of Nonlinear and Convex Analysis, 6(1), 117–136.

Combettes, P. L., & Pesquet, J. (2005). 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. https://doi.org/10.1109/icip.2004.1418755

Bauschke, H. H., Combettes, P. L., & Kruk, S. G. (2005). Extrapolation algorithm for affine-convex feasibility problems. Numerical Algorithms, 41(3), 239–274. https://doi.org/10.1007/s11075-005-9010-6

Capricelli, T. D., & Combettes, P. L. (2005). Parallel Block-Iterative Reconstruction Algorithms for Binary Tomography. Electronic Notes in Discrete Mathematics, 20, 263–280. https://doi.org/10.1016/j.endm.2005.05.068

Combettes, P. L., & Wajs, V. R. (2005). Signal Recovery by Proximal Forward-Backward Splitting. Multiscale Modeling & Simulation, 4(4), 1168–1200. https://doi.org/10.1137/050626090

Bauschke, H. H., Combettes, P. L., & Reich, S. (2005). The asymptotic behavior of the composition of two resolvents. Nonlinear Analysis: Theory, Methods & Applications, 60(2), 283–301. https://doi.org/10.1016/j.na.2004.07.054

Bauschke, H., Combettes, P., & Reich, S. (2005). The asymptotic behavior of the composition of two resolvents. Nonlinear Analysis, 60(2), 283–301. https://doi.org/10.1016/S0362-546X(04)00344-X

Combettes, P. L., & Wajs, V. R. (2005). 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. https://doi.org/10.1109/icip.2004.1419462

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

Combettes, P. L., & Pesquet, J.-C. (2004). 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. https://doi.org/10.1109/icassp.2004.1326382

Bauschke, H. H., Combettes, P. L., & Luke, D. R. (2004). Finding best approximation pairs relative to two closed convex sets in Hilbert spaces. Journal of Approximation Theory, 127(2), 178–192. https://doi.org/10.1016/j.jat.2004.02.006

Combettes, P. L., & Pesquet, J.-C. (2004). Image Restoration Subject to a Total Variation Constraint. IEEE Transactions on Image Processing, 13(9), 1213–1222. https://doi.org/10.1109/tip.2004.832922

Combettes, P. L., & Pennanen, T. (2004). Proximal Methods for Cohypomonotone Operators. SIAM Journal on Control and Optimization, 43(2), 731–742. https://doi.org/10.1137/s0363012903427336

Combettes, P. L. (2004). Solving monotone inclusions via compositions of nonexpansive averaged operators. Optimization, 53(5-6), 475–504. https://doi.org/10.1080/02331930412331327157

Combettes, P. L., & Pesquet, J. C. (2004). 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. https://doi.org/10.1109/icip.2003.1247259

Combettes, P. L., & Pesquet, J. C. (2004). Wavelet-constrained image restoration. International Journal of Wavelets, Multiresolution and Information Processing, 2(4), 371–389. https://doi.org/10.1142/s0219691304000688

Combettes, P. L. (2003). A block-iterative surrogate constraint splitting method for quadratic signal recovery. IEEE Transactions on Signal Processing, 51(7), 1771–1782. https://doi.org/10.1109/tsp.2003.812846

Bauschke, H. H., Borwein, J. M., & Combettes, P. L. (2003). Bregman Monotone Optimization Algorithms. SIAM Journal on Control and Optimization, 42(2), 596–636. https://doi.org/10.1137/s0363012902407120

Bauschke, H. H., & Combettes, P. L. (2003). Construction of best Bregman approximations in reflexive Banach spaces. Proceedings of the American Mathematical Society, 131(12), 3757–3766. https://doi.org/10.1090/s0002-9939-03-07050-3

Bauschke, H. H., Combettes, P. L., & Luke, D. R. (2003). Hybrid projection–reflection method for phase retrieval. Journal of the Optical Society of America A, 20(6), 1025. https://doi.org/10.1364/josaa.20.001025

Combettes, P. L., & Pesquet, J.-C. (2003). 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. https://doi.org/10.1109/isspa.2003.1224735

Bauschke, H. H., & Combettes, P. L. (2003). Iterating Bregman Retractions. SIAM Journal on Optimization, 13(4), 1159–1173. https://doi.org/10.1137/s1052623402410557

Bauschke, H. H., Combettes, P. L., & Luke, D. R. (2003). 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. https://doi.org/10.1109/icip.2002.1040082

Combettes, P. L. (2002). 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. https://doi.org/10.1109/icassp.1998.678136

Luo, J., & Combettes, P. L. (2002). 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. https://doi.org/10.1109/icassp.2000.861924

Combettes, P. L. (2002). 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. https://doi.org/10.1109/icassp.2000.861901

Combettes, P. L., & Luo, J. (2002). An adaptive level set method for nondifferentiable constrained image recovery. IEEE Transactions on Image Processing, 11(11), 1295–1304. https://doi.org/10.1109/tip.2002.804527

Combettes, P. L., & Pesquet, J.-C. (2002). 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. https://doi.org/10.1109/tfsa.1996.547473

Combettes, P. L. (2002). 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. https://doi.org/10.1109/icip.2001.959002

Combettes, P. L., & Pennanen, T. (2002). Generalized Mann iterates for constructing fixed points in Hilbert spaces. Journal of Mathematical Analysis and Applications, 275(2), 521–536. https://doi.org/10.1016/s0022-247x(02)00221-4

Combettes, P. L. (2002). 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. https://doi.org/10.1109/icip.1996.560883

Combettes, P. L., & Bondon, P. (2002). 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. https://doi.org/10.1109/icassp.1997.595313

Combettes, P. L., & Pesquet, J.-C. (2002). Nonlinear multiresolution image analysis via convex projections. Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269), 2, 762–765. https://doi.org/10.1109/icip.1998.723646

Puh, H., & Combettes, P. L. (2002). 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. https://doi.org/10.1109/icassp.1996.544812

Bauschke, H. H., Combettes, P. L., & Luke, D. R. (2002). Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization. Journal of the Optical Society of America A, 19(7), 1334. https://doi.org/10.1364/josaa.19.001334

Bauschke, H. H., & Combettes, P. L. (2001). A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces. Mathematics of Operations Research, 26(2), 248–264. https://doi.org/10.1287/moor.26.2.248.10558

Combettes, P. L. (2001). Convexité et signal. Actes du Congrès de Mathématiques Appliquées et Industrielles SMAI'01, 6–16.

Bauschke, H. H., Borwein, J. M., & Combettes, P. L. (2001). Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces. Communications in Contemporary Mathematics, 3(4), 615–647. https://doi.org/10.1142/s0219199701000524

Combettes, P. L. (2001). 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.

Combettes, P. L. (2001). On the numerical robustness of the parallel projection method in signal synthesis. IEEE Signal Processing Letters, 8(2), 45–47. https://doi.org/10.1109/97.895371

Combettes, P. L. (2001). Quasi-Fejérian Analysis of Some Optimization Algorithms. In Studies in Computational Mathematics (pp. 115–152). https://doi.org/10.1016/s1570-579x(01)80010-0

Combettes, P. L. (2000). Strong Convergence of Block-Iterative Outer Approximation Methods for Convex Optimization. SIAM Journal on Control and Optimization, 38(2), 538–565. https://doi.org/10.1137/s036301299732626x

Luo, J., & Combettes, P. L. (1999). A subgradient projection algorithm for nondifferentiable signal recovery. Proceedings of the IEEE Workshop on Nonlinear Signal and Image Processing, 452–456.

Combettes, P. L., & Bondon, P. (1999). Hard-constrained inconsistent signal feasibility problems. IEEE Transactions on Signal Processing, 47(9), 2460–2468. https://doi.org/10.1109/78.782189

Combettes, P. L., & Bondon, P. (1998). Constrained pulse shape synthesis for digital communications. Proceedings of the European Signal Processing Conference, 573–576.

Combettes, P. L., & Pesquet, J.-C. (1998). Convex multiresolution analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(12), 1308–1318. https://doi.org/10.1109/34.735804

Combettes, P. L. (1997). Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections. IEEE Transactions on Image Processing, 6(4), 493–506. https://doi.org/10.1109/83.563316

Combettes, P. L. (1997). Hilbertian convex feasibility problem: Convergence of projection methods. Applied Mathematics & Optimization, 35(3), 311–330. https://doi.org/10.1007/bf02683333

Combettes, P. L. (1996). Bounded-error models in inverse problems. Proceedings of the 1996 IMACS/IEEE MultiConference on Computational Engineering in Systems Applications, 2, 1023–1027.

Combettes, P. L., & Chaussalet, T. J. (1996). Combining statistical information in set theoretic estimation. IEEE Signal Processing Letters, 3(3), 61–62. https://doi.org/10.1109/97.481155

Puh, H., & Combettes, P. L. (1996). Set theoretic vector quantization. Proceedings of the Ninth IEEE Workshop on Image and Multidimensional Signal Processing, 48–49.

Combettes, P. L. (1996). The Convex Feasibility Problem in Image Recovery. In Advances in Imaging and Electron Physics (pp. 155–270). https://doi.org/10.1016/s1076-5670(08)70157-5

Pesquet, J.-C., & Combettes, P. L. (1996). Wavelet synthesis by alternating projections. IEEE Transactions on Signal Processing, 44(3), 728–732. https://doi.org/10.1109/78.489050

Combettes, P. L., & Bondon, P. (1995). Adaptive linear filtering with convex constraints. 1995 International Conference on Acoustics, Speech, and Signal Processing, 2, 1372–1375. https://doi.org/10.1109/icassp.1995.480496

Combettes, P. L. (1995). Constrained image recovery in a product space. Proceedings., International Conference on Image Processing, 2, 25–28. https://doi.org/10.1109/icip.1995.537406

Combettes, P. L. (1995). 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.

Combettes, P. L., & Trussell, H. J. (1995). Deconvolution with bounded uncertainty. International Journal of Adaptive Control and Signal Processing, 9(1), 3–17. https://doi.org/10.1002/acs.4480090103

Combettes, P. L. (1995). Restauration ensembliste d’images par itérations parallèles extrapolées de sous-gradients. In Actes du Quinzième Colloque GRETSI (pp. 447–450). Retrieved from http://hdl.handle.net/2042/12207

Bondon, P., Combettes, P. L., & Picinbono, B. (1995). Volterra filtering and higher order whiteness. IEEE Transactions on Signal Processing, 43(9), 2209–2212. https://doi.org/10.1109/78.414788

Combettes, P. L., & Puh, H. (1994). 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. https://doi.org/10.1109/icassp.1994.389385

Combettes, P. L. (1994). Convex set theoretic image recovery via chaotic iterations of approximate projections. Proceedings of 1st International Conference on Image Processing, 3, 182–186. https://doi.org/10.1109/icip.1994.413863

Combettes, P. L. (1994). Inconsistent signal feasibility problems: least-squares solutions in a product space. IEEE Transactions on Signal Processing, 42(11), 2955–2966. https://doi.org/10.1109/78.330356

Combettes, P. L., & Puh, H. (1994). Iterations of parallel convex projections in hilbert spaces. Numerical Functional Analysis and Optimization, 15(3-4), 225–243. https://doi.org/10.1080/01630569408816563

Combettes, P. L., & Chaussalet, T. J. (1994). Selecting Statistical Information In Set Theoretic Signal Processing. IEEE Seventh SP Workshop on Statistical Signal and Array Processing, 55–58. https://doi.org/10.1109/ssap.1994.572433

Combettes, P. L. (1994). Set Theoretic Signal Processing. IEEE Seventh SP Workshop on Statistical Signal and Array Processing, 1–6. https://doi.org/10.1109/ssap.1994.572418

Pesquet, J. C., & Combettes, P. L. (1994). Synthèse ensembliste d’ondelettes. Actes de la Conférence Temps-Fréquence, Ondelettes et Multirésolution, 14.1–14.10.

Combettes, P. L. (1993). 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.

Combettes, P. L., & Chaussalet, T. J. (1993). Estimation en présence de modèles incertains: sélection de formulations ensemblistes. In Actes du Quatorzième Colloque GRETSI (pp. 205–208). Retrieved from http://hdl.handle.net/2042/12154

Combettes, P. L., & Puh, H. (1993). 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. https://doi.org/10.1109/icassp.1993.319806

Combettes, P. L. (1993). Signal recovery by best feasible approximation. IEEE Transactions on Image Processing, 2(2), 269–271. https://doi.org/10.1109/83.217232

Combettes, P. L. (1993). The foundations of set theoretic estimation. Proceedings of the IEEE, 81(2), 182–208. https://doi.org/10.1109/5.214546

Bondon, P., Combettes, P. L., & Picinbono, B. (1993). 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. https://doi.org/10.1109/icassp.1993.319632

Zilovic, M. S., Roytman, L. M., Combettes, P. L., & Swamy, M. N. S. (1992). A bound for the zeros of polynomials. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 39(6), 476–478. https://doi.org/10.1109/81.153643

Combettes, P. L., Benidir, M., & Picinbono, B. (1992). 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. https://doi.org/10.1109/icassp.1992.226229

Combettes, P. L., & Trussell, H. J. (1992). Best stable and invertible approximations for ARMA systems. IEEE Transactions on Signal Processing, 40(12), 3066–3069. https://doi.org/10.1109/78.175751

Combettes, P. L. (1992). Convex set theoretic image recovery: History, current status, and new directions. Journal of Visual Communication and Image Representation, 3(4), 307–315. https://doi.org/10.1016/1047-3203(92)90034-q

Silverstein, J. W., & Combettes, P. L. (1992). 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. https://doi.org/10.1109/ssap.1992.246796

Silverstein, J. W., & Combettes, P. L. (1992). Signal detection via spectral theory of large dimensional random matrices. IEEE Transactions on Signal Processing, 40(8), 2100–2105. https://doi.org/10.1109/78.149981

Combettes, P. L., & Edmonson, W. W. (1992). What is a good estimate? Proceedings of the European Signal Processing Conference, 713–716.

Combettes, P. L., & Chaussalet, T. J. (1991). Critères de qualité en estimation ensembliste. Actes du Treizième Colloque GRETSI, 249–252. Juan-les-Pins.

Combettes, P. L., & Trussell, H. J. (1991). Set theoretic estimation by random search. IEEE Transactions on Signal Processing, 39(7), 1669–1671. https://doi.org/10.1109/78.134403

Combettes, P. L., & Civanlar, M. R. (1991). 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. https://doi.org/10.1109/icassp.1991.151014

Combettes, P. L., & Trussell, H. J. (1991). The use of noise properties in set theoretic estimation. IEEE Transactions on Signal Processing, 39(7), 1630–1641. https://doi.org/10.1109/78.134400

Combettes, P. L., & Trussell, H. J. (1990). Method of successive projections for finding a common point of sets in metric spaces. Journal of Optimization Theory and Applications, 67(3), 487–507. https://doi.org/10.1007/bf00939646

Combettes, P. L., & Trussell, H. J. (1990). New methods for the synthesis of set theoretic estimates (digital signal processing). International Conference on Acoustics, Speech, and Signal Processing, 2531–2534. https://doi.org/10.1109/icassp.1990.116116

Combettes, P. L., & Trussell, H. J. (1990). 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. https://doi.org/10.1109/spect.1990.205587

Combettes, P. L., & Trussell, H. J. (1989). General order moments in set theoretic estimation. International Conference on Acoustics, Speech, and Signal Processing, 2531–2534. https://doi.org/10.1109/icassp.1989.266876

Combettes, P. L., & Trussell, H. J. (1989). Methods for digital restoration of signals degraded by a stochastic impulse response. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(3), 393–401. https://doi.org/10.1109/29.21706

Combettes, P. L., & Trussell, H. J. (1988). Stability of the linear prediction filter: a set theoretic approach. ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing, 2288–2291. https://doi.org/10.1109/icassp.1988.197094

Trussell, H., & Combettes, P. (1987). Considerations for the restoration of stochastic degradations. ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing, 1209–1212. https://doi.org/10.1109/icassp.1987.1169769

Combettes, P. L., & Trussell, H. J. (1987). Modèles et algorithmes en vue de la restauration numérique d’images rayons-X. Actes du Colloque MARI-Cognitiva Electronic Image, 146–151.