photo

Patrick L. Combettes

Distinguished Professor, IEEE Fellow, SIAM Fellow
Department of Mathematics
North Carolina State University

  SAS Hall 3276
  +1 (919) 515-2671
  [my3initials]@math.ncsu.edu

book Corrected 2nd ed., 2019




Prox repository



Maths at NC State




Prox. repository



Maths at NC State

Biography

Editorial boards

Scientific awards

Administrative positions

Academic positions

Publications

[PRx]
[Bx]
[Dx]
[Jx]
[Ex]
[Cx]
[Sx] 		Preprint
Book
Edited book
Journal article
Book chapter
Conference proceedings paper
Guest edition of a special issue of a journal

Preprints

[PR6] P. L. Combettes and J. I. Madariaga, Randomly activated proximal methods for nonsmooth convex minimization. [arXiv]
[PR5] P. L. Combettes and D. J. Cornejo, Signal recovery with proximal comixtures. [arXiv]
[PR4] M. N. Bùi and P. L. Combettes, Integral resolvent and proximal mixtures. [arXiv]
[PR3] M. N. Bùi and P. L. Combettes, Hilbert direct integrals of monotone operators. [arXiv]
[PR2] M. N. Bùi and P. L. Combettes, Interchange rules for integral functions. [arXiv]
[PR1] L. M. Briceño-Arias, P. L. Combettes, and F. J. Silva, Proximity operators of perspective functions with nonlinear scaling. [arXiv]

2024

[J106] P. L. Combettes, The geometry of monotone operator splitting methods, Acta Numerica, to appear. [pdf]
[J105] L. M. Briceño-Arias, P. L. Combettes, and F. J. Silva, Perspective functions with nonlinear scaling, Communications in Contemporary Mathematics, to appear. [pdf]

2023

[J104] L. M. Briceño-Arias and P. L. Combettes, A perturbation framework for convex minimization and monotone inclusion problems with nonlinear compositions, Mathematics of Operations Research, published online 2023-10-17. [pdf]
[J103] P. L. Combettes, Resolvent and proximal compositions, Set-Valued and Variational Analysis, vol. 31, no. 3, art. 22, 29 pp., September 2023. [pdf]
[C62] P. L. Combettes, J.-C. Pesquet, and A. Repetti, A variational inequality model for learning neural networks, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 5 pp. Rhodes Island, Greece, June 4–10, 2023. [pdf]

2022

[J102] M. N. Bùi and P. L. Combettes, Analysis and numerical solution of a modular convex Nash equilibrium problem, Journal of Convex Analysis, vol. 29, no. 4, pp. 1007–1021, December 2022. [pdf]
[J101] M. N. Bùi and P. L. Combettes, Multivariate monotone inclusions in saddle form, Mathematics of Operations Research, vol. 47, no. 2, pp. 1082–1109, May 2022. [pdf]
[J100] P. L. Combettes and Z. C. Woodstock, A variational inequality model for the construction of signals from inconsistent nonlinear equations, SIAM Journal on Imaging Sciences, vol. 15, no. 1, pp. 84–109, January 2022. [pdf]
[C61] M. N. Bùi, P. L. Combettes, and Z. C. Woodstock, Block-activated algorithms for multicomponent fully nonsmooth minimization, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 5428–5432. Singapore, May 22–27, 2022. [pdf]
[C60] P. L. Combettes and Z. C. Woodstock, Signal recovery from inconsistent nonlinear observations, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 5872–5876. Singapore, May 22–27, 2022.

2021

[J99] M. N. Bùi and P. L. Combettes, Bregman forward-backward operator splitting, Set-Valued and Variational Analysis, vol. 29, no. 3, pp. 583–603, September 2021. [pdf]
[J98] P. L. Combettes and J.-C. Pesquet, Fixed point strategies in data science, IEEE Transactions on Signal Processing, vol. 69, pp. 3878–3905, August 2021. [pdf]
[J97] P. L. Combettes and Z. C. Woodstock, Reconstruction of functions from prescribed proximal points, Journal of Approximation Theory, vol. 268, art. 105606, 26 pp., August 2021. [pdf]
[J96] P. L. Combettes and C. L. Müller, Regression models for compositional data: General log-contrast formulations, proximal optimization, and microbiome data applications, Statistics in Biosciences, vol. 13, no. 2, pp. 217–242, July 2021. [pdf]
[J95] P. L. Combettes and L. E. Glaudin, Solving composite fixed point problems with block updates, Advances in Nonlinear Analysis, vol. 10, pp. 1154–1177, March 2021. [pdf]
[C59] P. L. Combettes and Z. C. Woodstock, A fixed point framework for recovering signals from nonlinear transformations, Proceedings of the European Signal Processing Conference, pp. 2120–2124. Amsterdam, The Netherlands, January 18–22, 2021. [pdf]

2020

[J94] M. N. Bùi and P. L. Combettes, Warped proximal iterations for monotone inclusions, Journal of Mathematical Analysis and Applications, vol. 491, no. 1, art. 124315, 21 pp., November 2020. [pdf]
[J93] P. L. Combettes and J.-C. Pesquet, Deep neural network structures solving variational inequalities, Set-Valued and Variational Analysis, vol. 28, no. 3, pp. 491–518, September 2020. [pdf]
[J92] P. L. Combettes and J.-C. Pesquet, Lipschitz certificates for layered network structures driven by averaged activation operators, SIAM Journal on Mathematics of Data Science, vol. 2, no. 2, pp. 529–557, June 2020. [pdf]
[J91] M. N. Bùi and P. L. Combettes, The Douglas-Rachford algorithm converges only weakly, SIAM Journal on Control and Optimization, vol. 58, no. 2, pp. 1118–1120, April 2020. [pdf]
[J90] P. L. Combettes and C. L. Müller, Perspective maximum likelihood-type estimation via proximal decomposition, Electronic Journal of Statistics, vol. 14, no. 1, pp. 207–238, January 2020. [pdf]

2019

[J89] P. L. Combettes and L. E. Glaudin, Proximal activation of smooth functions in splitting algorithms for convex image recovery, SIAM Journal on Imaging Sciences, vol. 12, no. 4, pp. 1905–1935, November 2019. [pdf]
[J88] P. L. Combettes, A. M. McDonald, C. A. Micchelli, and M. Pontil, Learning with optimal interpolation norms, Numerical Algorithms, vol. 81, no. 2, pp. 695–717, June 2019. [pdf]
[J87] P. L. Combettes and J.-C. Pesquet, Stochastic quasi-Fejér block-coordinate fixed point iterations with random sweeping II: Mean-square and linear convergence, Mathematical Programming, vol. B174, no. 1, pp. 433–451, April 2019. [pdf]
[C58] P. L. Combettes and L. E. Glaudin, Fully proximal splitting algorithms in image recovery, Proceedings of the European Signal Processing Conference, pp. 525-529. A Coruña, Spain, September 2–6, 2019.

2018

[J86] P. L. Combettes, Monotone operator theory in convex optimization, Mathematical Programming, vol. B170, no. 1, pp. 177–206, July 2018. [pdf]
[J85] P. L. Combettes, Perspective functions: Properties, constructions, and examples, Set-Valued and Variational Analysis, vol. 26, no. 2, pp. 247–264, June 2018. [pdf]
[J84] P. L. Combettes and J. Eckstein, Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions, Mathematical Programming, vol. B168, no. 1, pp. 645–672, March 2018. [pdf]
[J83] P. L. Combettes and C. L. Müller, Perspective functions: Proximal calculus and applications in high-dimensional statistics, Journal of Mathematical Analysis and Applications, vol. 457, no. 2, pp. 1283–1306, January 2018. [pdf]
[J82] P. L. Combettes, S. Salzo, and S. Villa, Regularized learning schemes in feature Banach spaces, Analysis and Applications, vol. 16, no. 1, pp. 1–54, January 2018. [pdf]
[J81] P. L. Combettes, S. Salzo, and S. Villa, Consistent learning by composite proximal thresholding, Mathematical Programming, vol. B167, no. 1, pp. 99–127, January 2018. [pdf]
[C57] P. L. Combettes and J.-C. Pesquet, Linear convergence of stochastic block-coordinate fixed point algorithms, Proceedings of the European Signal Processing Conference, pp. 747–751. Rome, Italy, September 3–7, 2018.

2017

[B02] H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, second edition. Springer, New York, 2017. [pdf]
[J80] P. L. Combettes and L. E. Glaudin, Quasinonexpansive iterations on the affine hull of orbits: From Mann's mean value algorithm to inertial methods, SIAM Journal on Optimization, vol. 27, no. 4, pp. 2356–2380, December 2017. [pdf]
[J79] M. Barlaud, W. Belhajali, P. L. Combettes, and L. Fillatre, Classification and regression using an outer approximation projection-gradient method, IEEE Transactions on Signal Processing, vol. 65, no. 17, pp. 4635–4644, September 2017. [pdf]

2016

[J78] H. Attouch, L. M. Briceño-Arias, and P. L. Combettes, A strongly convergent primal-dual method for nonoverlapping domain decomposition, Numerische Mathematik, vol. 133, no. 3, pp. 433–470, July 2016. [pdf]
[J77] P. L. Combettes and Q. V. Nguyen, Solving composite monotone inclusions in reflexive Banach spaces by constructing best Bregman approximations from their Kuhn-Tucker set, Journal of Convex Analysis, vol. 23, no. 2, pp. 481–510, May 2016. Special issue dedicated to the memory of Jean Jacques Moreau. [pdf]
[J76] P. L. Combettes and Đinh Dũng, Kolmogorov n-widths of function classes induced by a non-degenerate differential operator: A convex duality approach, Set-Valued and Variational Analysis, vol. 24, no. 1, pp. 83–99, March 2016. [pdf]
[J75] P. L. Combettes and J.-C. Pesquet, Stochastic approximations and perturbations in forward-backward splitting for monotone operators, Pure and Applied Functional Analysis, vol. 1, no. 1, pp. 13–37, January 2016. [pdf]
[C56] P. L. Combettes and J.-C. Pesquet, Stochastic forward-backward and primal-dual approximation algorithms with application to online image restoration, Proceedings of the European Signal Processing Conference, 5 pages. Budapest, Hungary, August 29-September 3, 2016. [pdf]

2015

[J74] A. Alotaibi, P. L. Combettes, and N. Shahzad, Best approximation from the Kuhn-Tucker set of composite monotone inclusions, Numerical Functional Analysis and Optimization, vol. 36, no. 12, pp. 1513–1532, December 2015. [pdf]
[J73] P. L. Combettes and J.-C. Pesquet, Stochastic quasi-Fejér block-coordinate fixed point iterations with random sweeping, SIAM Journal on Optimization, vol. 25, no. 2, pp. 1221–1248, July 2015. [pdf]
[J72] P. L. Combettes and I. Yamada, Compositions and convex combinations of averaged nonexpansive operators, Journal of Mathematical Analysis and Applications, vol. 425, no. 1, pp. 55–70, May 2015. [pdf]

2014

[S01] P. L. Combettes, J.-B. Hiriart-Urruty, and M. Théra (Guest editors), Modern convex analysis, Mathematical Programming, vol. B148, nos. 1–2, December 2014. [pdf]
[J71] A. Alotaibi, P. L. Combettes, and N. Shahzad, Solving coupled composite monotone inclusions by successive Fejér approximations of their Kuhn-Tucker set, SIAM Journal on Optimization, vol. 24, no. 4, pp. 2076–2095, December 2014. [pdf]
[J70] M. A. Alghamdi, A. Alotaibi, P. L. Combettes, and N. Shahzad, A primal-dual method of partial inverses for composite inclusions, Optimization Letters, vol. 8, no. 8, pp. 2271–2284, December 2014. [pdf]
[J69] P. L. Combettes and B. C. Vũ, Variable metric forward-backward splitting with applications to monotone inclusions in duality, Optimization, vol. 63, no. 9, pp. 1289–1318, September 2014. [pdf] (published online 2012-12-13)
[J68] J.-B. Baillon, P. L. Combettes, and R. Cominetti, Asymptotic behavior of compositions of under-relaxed nonexpansive operators, Journal of Dynamics and Games, vol. 1, no. 3, pp. 331–346, July 2014. [pdf]
[J67] S. R. Becker and P. L. Combettes, An algorithm for splitting parallel sums of linearly composed monotone operators, with applications to signal recovery, Journal of Nonlinear and Convex Analysis, vol. 15, no. 1, pp. 137–159, January 2014. [pdf]
[C55] P. L. Combettes, L. Condat, J.-C. Pesquet, and B. C. Vũ, A forward-backward view of some primal-dual optimization methods in image recovery, Proceedings of the IEEE International Conference on Image Processing. Paris, France, October 27–30, 2014. [pdf]

2013

[J66] P. L. Combettes, Systems of structured monotone inclusions: Duality, algorithms, and applications, SIAM Journal on Optimization, vol. 23, no. 4, pp. 2420–2447, December 2013. [pdf]
[J65] P. L. Combettes and N. N. Reyes, Moreau's decomposition in Banach spaces, Mathematical Programming, vol. 139, no. 1, pp. 103–114, June 2013. [pdf]
[J64] P. L. Combettes and B. C. Vũ, Variable metric quasi-Fejér monotonicity, Nonlinear Analysis: Theory, Methods, and Applications, vol. 78, pp. 17–31, February 2013. [pdf]
[E05] L. M. Briceño-Arias and P. L. Combettes, Monotone operator methods for Nash equilibria in non-potential games, in: Computational and Analytical Mathematics, (D. Bailey, H. H. Bauschke, P. Borwein, F. Garvan, M. Théra, J. Vanderwerff, and H. Wolkowicz, Editors), pp. 143–159. Springer, New York, 2013. [pdf]

2012

[J63] P. L. Combettes and J.-C. Pesquet, Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators, Set-Valued and Variational Analysis, vol. 20, no. 2, pp. 307–330, June 2012. [pdf]
[J62] Y. Censor, W. Chen, P. L. Combettes, R. Davidi, and G. T. Herman, On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints, Computational Optimization and Applications, vol. 51, no. 3, pp. 1065–1088, April 2012. [pdf]
[J61] J.-B. Baillon, P. L. Combettes, and R. Cominetti, There is no variational characterization of the cycles in the method of periodic projections, Journal of Functional Analysis, vol. 262, no. 1, pp. 400–408, January 2012. [pdf]

2011

[B02] H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York, 2011. [pdf excerpt]
[J60] L. M. Briceño-Arias and P. L. Combettes, A monotone+skew splitting model for composite monotone inclusions in duality, SIAM Journal on Optimization, vol. 21, no. 4, pp. 1230–1250, October 2011. [pdf]
[J59] L. M. Briceño-Arias, P. L. Combettes, J.-C. Pesquet, and N. Pustelnik, Proximal algorithms for multicomponent image recovery problems, Journal of Mathematical Imaging and Vision, vol. 41, no. 1, pp. 3–22, September 2011. [pdf]
[J58] P. L. Combettes, Đinh Dũng, and B. C. Vũ, Proximity for sums of composite functions, Journal of Mathematical Analysis and Applications, vol. 380, no. 2, pp. 680–688, August 2011. [pdf]
[E04] P. L. Combettes and J.-C. Pesquet, Proximal splitting methods in signal processing, in: Fixed-Point Algorithms for Inverse Problems in Science and Engineering, (H. H. Bauschke, R. S. Burachik, P. L. Combettes, V. Elser, D. R. Luke, and H. Wolkowicz, Editors), pp. 185–212. Springer, New York, 2011. [pdf]
[D01] H. H. Bauschke, R. S. Burachik, P. L. Combettes, V. Elser, D. R. Luke, and H. Wolkowicz (Editors), Fixed-Point Algorithms for Inverse Problems in Science and Engineering. Springer, New York, 2011.

2010

[J57] P. L. Combettes, Đinh Dũng, and B. C. Vũ, Dualization of signal recovery problems, Set-Valued and Variational Analysis, vol. 18, pp. 373–404, December 2010. [pdf]
[J56] H. H. Bauschke and P. L. Combettes, The Baillon-Haddad theorem revisited, Journal of Convex Analysis, vol. 17, no. 4, pp. 781–787, December 2010. [pdf]
[J55] P. L. Combettes and N. N. Reyes, Functions with prescribed best linear approximations, Journal of Approximation Theory, vol. 162, no. 5, pp. 1095–1116, May 2010. [pdf]
[J54] H. Attouch, L. M. Briceño-Arias, and P. L. Combettes, A parallel splitting method for coupled monotone inclusions, SIAM Journal on Control and Optimization, vol. 48, no. 5, pp. 3246–3270, January 2010. [pdf]
[C54] L. M. Briceño-Arias, P. L. Combettes, J.-C. Pesquet, and N. Pustelnik, Proximal method for geometry and texture image decomposition, Proceedings of the IEEE International Conference on Image Processing. Hong-Kong, September 26–29, 2010.
[C53] J. Bolte, P. L. Combettes, and J.-C. Pesquet, Alternating proximal algorithm for blind image recovery, Proceedings of the IEEE International Conference on Image Processing. Hong-Kong, September 26–29, 2010. [pdf]

2009

[J53] P. L. Combettes, Iterative construction of the resolvent of a sum of maximal monotone operators, Journal of Convex Analysis, vol. 16, no. 4, pp. 727-748, December 2009. [pdf]
[J52] L. M. Briceño-Arias and P. L. Combettes, Convex variational formulation with smooth coupling for multicomponent signal decomposition and recovery, Numerical Mathematics: Theory, Methods, and Applications, vol. 2, no. 4, pp. 485–508, November 2009. [pdf]
[C52] P. L. Combettes and J.-C. Pesquet, Split convex minimization algorithm for signal recovery, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 685–688. Taipei, Taiwan, April 19–24, 2009.

2008

[J51] P. L. Combettes and J.-C. Pesquet, A proximal decomposition method for solving convex variational inverse problems, Inverse Problems, vol. 24, no. 6, article ID 065014, 27 pp., December 2008. [pdf]
[J50] H. H. Bauschke and P. L. Combettes, A Dykstra-like algorithm for two monotone operators, Pacific Journal of Optimization, vol. 4, no. 3, pp. 383–391, September 2008. [pdf]
[J49] P. L. Combettes and S. A. Hirstoaga, Visco-penalization of the sum of two monotone operators, Nonlinear Analysis: Theory, Methods, and Applications, vol. 69, no. 2, pp. 579–591, July 2008. [pdf]

2007

[J48] P. L. Combettes and J.-C. Pesquet, A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery, IEEE Journal of Selected Topics in Signal Processing, vol. 1, no. 4, pp. 564–574, December 2007. [pdf]
[J47] P. L. Combettes and J.-C. Pesquet, Proximal thresholding algorithm for minimization over orthonormal bases, SIAM Journal on Optimization, vol. 18, no. 4, pp. 1351–1376, November 2007. [pdf]
[J46] C. Chaux, P. L. Combettes, J.-C. Pesquet, and V. R. Wajs, A variational formulation for frame-based inverse problems, Inverse Problems, vol. 23, no. 4, pp. 1495–1518, August 2007. [pdf]
[E03] T. D. Capricelli and P. L. Combettes, A convex programming algorithm for noisy discrete tomography, in: Advances in Discrete Tomography and Its Applications, (G. T. Herman and A. Kuba, Editors), pp. 207–226. Boston, MA: Birkhäuser, 2007. [pdf]
[C51] C. Chaux, P. L. Combettes, J.-C. Pesquet, and V. R. Wajs, Opérateurs proximaux pour la restauration bayésienne de signaux, Proceedings of the 21st GRETSI Symposium, pp. 1277–1280. Troyes, France, 11–14 Septembre 2007.
[C50] P. L. Combettes and J.-C. Pesquet, Sparse signal recovery by iterative proximal thresholding, Proceedings of the 15th European Signal Processing Conference, 4 pages. Poznan, Poland, September 3–7, 2007.

2006

[J45] P. L. Combettes and S. A. Hirstoaga, Approximating curves for nonexpansive and monotone operators, Journal of Convex Analysis, vol. 13, nos. 3–4, pp. 633–646, December 2006. [pdf]
[J44] H. H. Bauschke, P. L. Combettes, and D. Noll, Joint minimization with alternating Bregman proximity operators, Pacific Journal of Optimization, vol. 2, no. 3, pp. 401–424, September 2006. [pdf]
[J43] H. H. Bauschke, P. L. Combettes, and D. R. Luke, 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, vol. 141, no. 1, pp. 63–69, July 2006. [pdf]
[J42] H. H. Bauschke, P. L. Combettes, and S. G. Kruk, Extrapolation algorithm for affine-convex feasibility problems, Numerical Algorithms, vol. 41, no. 3, pp. 239–274, March 2006. [pdf]
[C49] C. Chaux, P. L. Combettes, J.-C. Pesquet, and V. R. Wajs, Iterative image deconvolution using overcomplete representations, Proceedings of the 14th European Signal Processing Conference, 4 pages. Florence, Italy, September 4–8, 2006.
[C48] H. H. Bauschke, P. L. Combettes, and J.-C. Pesquet, A decomposition method for nonsmooth convex variational signal recovery, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 989–992. Toulouse, France, May 14–19, 2006.

2005

[J41] P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Modeling and Simulation, vol. 4, no. 4, pp. 1168–1200, November 2005. [pdf]
[J40] P. L. Combettes and S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, Journal of Nonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, April 2005. [pdf]
[J39] H. H. Bauschke, P. L. Combettes, and S. Reich, The asymptotic behavior of the composition of two resolvents, Nonlinear Analysis: Theory, Methods, and Applications, vol. 60, no. 2, pp. 283–301, January 2005. [pdf]
[C47] C. Chaux, P. L. Combettes, J.-C. Pesquet, and V. R. Wajs, A forward-backward algorithm for image restoration with sparse representations, Proceedings of the International Conference on Signal Processing with Adaptative Sparse Structured Representations, pp. 49–52. Rennes, France, November 16–18, 2005.
[C46] T. D. Capricelli and P. L. Combettes, Éclatement des contraintes en reconstruction tomographique, Proceedings of the 20th GRETSI Symposium, pp. 655–658. Louvain-la-Neuve, Belgium, 6–9 Septembre 2005.
[C45] T. D. Capricelli and P. L. Combettes, Parallel block-iterative reconstruction algorithms for binary tomography, Electronic Notes in Discrete Mathematics, vol. 20, pp. 263–280, July 2005.
[C44] H. H. Bauschke, P. L. Combettes, and D. R. Luke, A new generation of iterative transform algorithms for phase contrast tomography, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, pp. 89–92. Philadelphia, PA, March 19–23, 2005.

2004

[J38] P. L. Combettes, Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, vol. 53, no. 5–6, pp. 475–504, December 2004. [pdf]
[J37] P. L. Combettes and J. C. Pesquet, Wavelet-constrained image restoration, International Journal of Wavelets, Multiresolution, and Information Processing, vol. 2, no. 4, pp. 371–389, December 2004. [pdf]
[J36] P. L. Combettes and T. Pennanen, Proximal methods for cohypomonotone operators, SIAM Journal on Control and Optimization, vol. 43, no. 2, pp. 731–742, October 2004. [pdf]
[J35] P. L. Combettes and J. C. Pesquet, Image restoration subject to a total variation constraint, IEEE Transactions on Image Processing, vol. 13, no. 9, pp. 1213–1222, September 2004. [pdf]
[J34] H. H. Bauschke, P. L. Combettes, and D. R. Luke, Finding best approximation pairs relative to two closed convex sets in Hilbert spaces, Journal of Approximation Theory, vol. 127, no. 2, pp. 178–192, March 2004. [pdf]
[C43] P. L. Combettes and V. R. Wajs, Theoretical analysis of some regularized image denoising methods, Proceedings of the IEEE International Conference on Image Processing, vol. 1, pp. 969–972. Singapore, October 24–27, 2004.
[C42] P. L. Combettes and J. C. Pesquet, Estimating first-order finite-difference information in image restoration problems, Proceedings of the IEEE International Conference on Image Processing, vol. 1, pp. 321–324. Singapore, October 24–27, 2004.
[C41] P. L. Combettes and J. C. Pesquet, Constraint construction in convex set theoretic signal recovery via Stein's principle, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 2, pp. 813–816. Montréal, Canada, May 17–21, 2004.

2003

[J33] H. H. Bauschke and P. L. Combettes, Construction of best Bregman approximations in reflexive Banach spaces, Proceedings of the American Mathematical Society, vol. 131, no. 12, pp. 3757–3766, December 2003. [pdf]
[J32] P. L. Combettes, A block-iterative surrogate constraint splitting method for quadratic signal recovery, IEEE Transactions on Signal Processing, vol. 51, no. 7, pp. 1771–1782, July 2003. [pdf]
[J31] H. H. Bauschke, J. M. Borwein, and P. L. Combettes, Bregman monotone optimization algorithms, SIAM Journal on Control and Optimization, vol. 42, no. 2, pp. 596–636, June 2003. [pdf]
[J30] H. H. Bauschke, P. L. Combettes, and D. R. Luke, Hybrid projection-reflection method for phase retrieval, Journal of the Optical Society of America A, vol. 20, no. 6, pp. 1025–1034, June 2003. [pdf]
[J29] H. H. Bauschke and P. L. Combettes, Iterating Bregman retractions, SIAM Journal on Optimization, vol. 13, no. 4, pp. 1159–1173, April 2003. [pdf]
[C40] P. L. Combettes and J. C. Pesquet, Image deconvolution with total variation bounds, Proceedings of the Seventh International Symposium on Signal Processing and Its Applications, vol. 1, pp. 441–444. Paris, France, July 1–4, 2003.
[C39] P. L. Combettes and J. C. Pesquet, Incorporating total variation information in image recovery, Proceedings of the IEEE International Conference on Image Processing, vol. 3, pp. 373–376. Barcelona, Spain, September 14–17, 2003.

2002

[J28] P. L. Combettes and T. Pennanen, Generalized Mann iterates for constructing fixed points in Hilbert spaces, Journal of Mathematical Analysis and Applications, vol. 275, no. 2, pp. 521–536, November 2002. [pdf]
[J27] P. L. Combettes and J. Luo, An adaptive level set method for nondifferentiable constrained image recovery, IEEE Transactions on Image Processing, vol. 11, no. 11, pp. 1295–1304, November 2002. [pdf]
[J26] H. H. Bauschke, P. L. Combettes, and D. R. Luke, Phase retrieval, error reduction algorithm, and Fienup variants: A view from convex optimization, Journal of the Optical Society of America A, vol. 19, no. 7, pp. 1334–1345, July 2002. [pdf]
[C38] H. H. Bauschke, P. L. Combettes, and D. R. Luke, On the structure of some phase retrieval algorithms, Proceedings of the IEEE International Conference on Image Processing, vol. 2, pp. 841–844. Rochester, NY, September 22–25, 2002.

2001

[J25] H. H. Bauschke, J. M. Borwein, and P. L. Combettes, Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces, Communications in Contemporary Mathematics, vol. 3, no. 4, pp. 615–647, 2001. [pdf]
[J24] H. H. Bauschke and P. L. Combettes, A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces, Mathematics of Operations Research, vol. 26, no. 2, pp. 248–264, May 2001. [pdf]
[J23] P. L. Combettes, On the numerical robustness of the parallel projection method in signal synthesis, IEEE Signal Processing Letters, vol. 8, no. 2, pp. 45–47, February 2001.
[E02] P. L. Combettes, Quasi-Fejérian analysis of some optimization algorithms, in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, (D. Butnariu, Y. Censor, and S. Reich, Eds.), pp. 115–152. New York: Elsevier, 2001. [pdf]
[E01] P. L. Combettes, Fejér-monotonicity in convex optimization, in Encyclopedia of Optimization (C. A. Floudas and P. M. Pardalos, Eds.), vol. 2, pp. 106–114. Springer-Verlag, New York, 2001. [pdf]
[C37] P. L. Combettes, Convex set theoretic image recovery with inexact projection algorithms, Proceedings of the IEEE International Conference on Image Processing, vol. 1, pp. 257–260. Thessaloniki, Greece, October 7–10, 2001.
[C36] P. L. Combettes, Convexité et signal, Actes du Congrès de Mathématiques Appliquées et Industrielles SMAI'01, pp. 6–16. Pompadour, France, May 28-June 1, 2001. [pdf]

2000

[J22] P. L. Combettes, Strong convergence of block-iterative outer approximation methods for convex optimization, SIAM Journal on Control and Optimization , vol. 38, no. 2, pp. 538–565, February 2000. [pdf]
[C35] P. L. Combettes, A parallel constraint disintegration and approximation scheme for quadratic signal recovery, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 1, pp. 165–168. Istanbul, Turkey, June 5–9, 2000.
[C34] J. Luo and P. L. Combettes, A level-set subgradient projection algorithm for non-differentiable signal restoration with multiple constraints, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 1, pp. 225–228. Istanbul, Turkey, June 5–9, 2000.

1999

[J21] P. L. Combettes and P. Bondon, Hard-constrained inconsistent signal feasibility problems, IEEE Transactions on Signal Processing, vol. 47, no. 9, pp. 2460–2468, September 1999. [pdf]
[C33] J. Luo and P. L. Combettes, A subgradient projection algorithm for nondifferentiable signal recovery, Proceedings of the IEEE Workshop on Nonlinear Signal and Image Processing, pp. 452–456. Antalya, Turkey, June 20–23, 1999.

1998

[J20] P. L. Combettes and J. C. Pesquet, Convex multiresolution analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 12, pp. 1308–1318, December 1998. Gzipped PostScript
[C32] P. L. Combettes and J. C. Pesquet, Nonlinear multiresolution image analysis via convex projections, Proceedings of the IEEE International Conference on Image Processing, vol. 2, pp. 762–765. Chicago, IL, October 4–7, 1998.
[C31] P. L. Combettes and P. Bondon, Constrained pulse shape synthesis for digital communications, Proceedings of the European Signal Processing Conference, pp. 573–576. Island of Rhodes, Greece, September 8–11, 1998.
[C30] P. L. Combettes, A block-iterative quadratic signal recovery algorithm, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 2917–2920. Seattle, WA, May 12–15, 1998.

1997

[J19] P. L. Combettes, Hilbertian convex feasibility problem: Convergence of projection methods, Applied Mathematics and Optimization, vol. 35, no. 3, pp. 311–330, May 1997. [pdf]
[J18] P. L. Combettes, Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections, IEEE Transactions on Image Processing, vol. 6, no. 4, pp. 493–506, April 1997. [pdf]
[C29] P. L. Combettes and P. Bondon, Hard-constrained signal feasibility problems, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, pp. 2569–2572. Munich, Germany, April 21–24, 1997.

1996

[J17] P. L. Combettes and T. J. Chaussalet, Combining statistical information in set theoretic estimation, IEEE Signal Processing Letters, vol. 3, no. 3, pp. 61–62, March 1996. [Gzipped PostScript]
[J16] J. C. Pesquet and P. L. Combettes, Wavelet synthesis by alternating projections, IEEE Transactions on Signal Processing, vol. 44, no. 3, pp. 728–732, March 1996.
[B01] P. L. Combettes, The Convex Feasibility Problem in Image Recovery, vol. 95 of Advances in Imaging and Electron Physics, Academic Press, New York, 1996. [pdf]
[C28] P. L. Combettes, Generalized convex set theoretic image recovery, Proceedings of the IEEE International Conference on Image Processing, vol. 2, pp. 453–456. Lausanne, Switzerland, September 16–19, 1996.
[C27] P. L. Combettes, Bounded-error models in inverse problems, Proceedings of the 1996 IMACS/IEEE MultiConference on Computational Engineering in Systems Applications, vol. 2, pp. 1023–1027. Lille, France, July 9–12, 1996.
[C26] P. L. Combettes and J. C. Pesquet, Convex multiresolution analysis, Proceedings of the IEEE International Symposium on Time-Frequency and Time-Scale Analysis, pp. 301–304. Paris, France, June 18–21, 1996.
[C25] H. Puh and P. L. Combettes, Operator theoretic image coding, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, pp. 1863–1866. Atlanta, GA, May 7–10, 1996.
[C24] H. Puh and P. L. Combettes, Set theoretic vector quantization, Proceedings of the Ninth IEEE Workshop on Image and Multidimensional Signal Processing, pp. 48–49. Belize City, Belize, March 3–6, 1996.

1995

[J15] P. Bondon, P. L. Combettes, and B. Picinbono, Volterra filtering and higher order whiteness, IEEE Transactions on Signal Processing, vol. 43, no. 9, pp. 2209–2212, September 1995. [Gzipped PostScript]
[J14] P. L. Combettes, Construction d'un point fixe commun à une famille de contractions fermes, Comptes Rendus de l'Académie des Sciences de Paris, Série I (Mathématique) , vol. 320, no. 11, pp. 1385–1390, June 1995. [pdf]
[J13] P. L. Combettes and H. J. Trussell, Deconvolution with bounded uncertainty, International Journal of Adaptive Control and Signal Processing, vol. 9, no. 1, pp. 3–17, January 1995. [pdf]
[C23] P. L. Combettes, Constrained image recovery in a product space, Proceedings of the IEEE International Conference on Image Processing, vol. 2, pp. 25–28. Washington, DC, October 23–26, 1995.
[C22] P. L. Combettes, Restauration ensembliste d'images par itérations parallèles extrapolées de sous-gradients, Proceedings of the 15th GRETSI Symposium, pp. 447–450. Juan-les-Pins, France, September 18–22, 1995.
[C21] P. L. Combettes and P. Bondon, Adaptive linear filtering with convex constraints, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 2, pp. 1372–1375. Detroit, MI, May 8–12, 1995.

1994

[J12] P. L. Combettes, Inconsistent signal feasibility problems: Least-squares solutions in a product space, IEEE Transactions on Signal Processing, vol. 42, no. 11, pp. 2955–2966, November 1994. [pdf]
[J11] P. L. Combettes and H. Puh, Iterations of parallel convex projections in Hilbert spaces, Numerical Functional Analysis and Optimization, vol. 15, nos. 3–4, pp. 225–243, 1994.
[C20] P. L. Combettes, Convex set theoretic image recovery via chaotic iterations of approximate projections, Proceedings of the IEEE International Conference on Image Processing, vol. 3, pp. 182–186. Austin, TX, November 13–16, 1994.
[C19] P. L. Combettes and T. J. Chaussalet, Selecting statistical information in set theoretic signal processing, Proceedings of the Seventh IEEE Workshop on Statistical Signal and Array Processing, pp. 55–58. Québec City, Canada, June 26–29, 1994.
[C18] P. L. Combettes, Set theoretic signal processing, Proceedings of the Seventh IEEE Workshop on Statistical Signal and Array Processing, pp. 1–6. Québec City, Canada, June 26–29, 1994.
[C17] P. L. Combettes and H. Puh, A fast parallel projection algorithm for set theoretic image recovery, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 473–476. Adelaide, Australia, April 19–22, 1994.
[C16] J. C. Pesquet and P. L. Combettes, Synthèse ensembliste d'ondelettes, Proceedings of the Conference on Time-Frequency, Wavelets, and Multiresolution, pp. 14.1–14.10. Lyon, France, March 9–11, 1994.

1993

[J10] P. L. Combettes, Signal recovery by best feasible approximation, IEEE Transactions on Image Processing, vol. 2, no. 2, pp. 269–271, April 1993.
[J09] P. L. Combettes, The foundations of set theoretic estimation, Proceedings of the IEEE, vol. 81, no. 2, pp. 182–208, February 1993. [pdf]
[C15] P. L. Combettes and T. J. Chaussalet, Estimation en présence de modèles incertains: Sélection de formulations ensemblistes, Proceedings of the 14th GRETSI Symposium, pp. 205–208. Juan-les-Pins, France, September 13–16, 1993.
[C14] P. L. Combettes, A simultaneous projection method for inconsistent signal and image feasibility problems, Proceedings of the Eighth IEEE Workshop on Image and Multidimensional Signal Processing, pp. 32–33. Cannes, France, September 8–10, 1993.
[C13] P. L. Combettes and H. Puh, Parallel projection methods for set theoretic signal reconstruction and restoration, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 297–300. Minneapolis, MN, April 27–30, 1993.
[C12] P. Bondon, P. L. Combettes, and B. Picinbono, Volterra prediction models and higher order whiteness, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, pp. 212–215. Minneapolis, MN, April 27–30, 1993.

1992

[J08] P. L. Combettes, Convex set theoretic image recovery: History, current status, and new directions, Journal of Visual Communication and Image Representation, vol. 3, no. 4, pp. 307–315, December 1992.
[J07] P. L. Combettes and H. J. Trussell, Best stable and invertible approximations for ARMA systems, IEEE Transactions on Signal Processing, vol. 40, no. 12, pp. 3066–3069, December 1992.
[J06] J. W. Silverstein and P. L. Combettes, Signal detection via spectral theory of large dimensional random matrices, IEEE Transactions on Signal Processing, vol. 40, no. 8, pp. 2100–2105, August 1992. [pdf of long version]
[J05] M. S. Zilovic, L. M. Roytman, P. L. Combettes, and M. N. S. Swamy, A bound for the zeros of polynomials, IEEE Transactions on Circuits and Systems I, vol. 39, no. 6, pp. 476–478, June 1992.
[C11] J. W. Silverstein and P. L. Combettes, Large dimensional random matrix theory for signal detection and estimation in array processing, Proceedings of the Sixth IEEE Workshop on Statistical Signal and Array Processing, pp. 276–279. Victoria, BC, Canada, October 7–9, 1992.
[C10] P. L. Combettes and W. W. Edmonson, What is a good estimate?, Proceedings of the European Signal Processing Conference, pp. 713–716. Brussels, Belgium, August 24–27, 1992.
[C09] P. L. Combettes, M. Benidir, and B. Picinbono, A general framework for the incorporation of uncertainty in set theoretic estimation, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 3, pp. 349–352. San Francisco, CA, March 23–26, 1992.

1991

[J04] P. L. Combettes and H. J. Trussell, Set theoretic estimation by random search, IEEE Transactions on Signal Processing, vol. 39, no. 7, pp. 1669–1671, July 1991.
[J03] P. L. Combettes and H. J. Trussell, The use of noise properties in set theoretic estimation, IEEE Transactions on Signal Processing, vol. 39, no. 7, pp. 1630–1641, July 1991. [pdf]
[C08] P. L. Combettes and T. J. Chaussalet, Critères de qualité en estimation ensembliste, Proceedings of the 13th GRETSI Symposium, pp. 249–252. Juan-les-Pins, France, September 16–20, 1991.
[C07] P. L. Combettes and M. R. Civanlar, The foundations of set theoretic estimation, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 2921–2924. Toronto, Canada, May 14–17, 1991.

1990

[J02] P. L. Combettes and H. J. Trussell, Method of successive projections for finding a common point of sets in metric spaces, Journal of Optimization Theory and Applications, vol. 67, no. 3, pp. 487–507, December 1990. [pdf]
[C06] P. L. Combettes and H. J. Trussell, Set theoretic autoregressive spectral estimation, Proceedings of the Fifth IEEE ASSP Workshop on Spectrum Estimation and Modeling, pp. 261–264. Rochester, NY, October 10–12, 1990.
[C05] P. L. Combettes and H. J. Trussell, New methods for the synthesis of set theoretic estimates, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 2531–2534. Albuquerque, NM, April 3–6, 1990.

1989

[J01] P. L. Combettes and H. J. Trussell, Methods for digital restoration of signals degraded by a stochastic impulse response, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, no. 3, pp. 393–401, March 1989.
[C04] P. L. Combettes and H. J. Trussell, General order moments in set theoretic estimation, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 2531–2534. Glasgow, Scotland, May 23–26, 1989.

1988

[C03] P. L. Combettes and H. J. Trussell, Stability of the linear prediction filter: A set theoretic approach, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 2288–2291. New York, NY, April 11–14, 1988.

1987

[C02] P. L. Combettes and H. J. Trussell, Modèles et algorithmes en vue de la restauration numérique d'images rayons-X, Proceedings of MARI-Cognitiva Electronic Image, pp. 146–151. Paris, France, May 18–22, 1987. [pdf]
[C01] H. J. Trussell and P. L. Combettes, Considerations for the restoration of stochastic degradations, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 1209–1212. Dallas, TX, April 6–9, 1987.

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