H. Attouch and J. Bolte, On the convergence of the proximal algorithm for nonsmooth functions involving analytic features, Mathematical Programming, vol.4, issue.1-2, pp.5-16, 2009.
DOI : 10.1007/s10107-007-0133-5

URL : https://hal.archives-ouvertes.fr/hal-00803898

H. Attouch, J. Bolte, P. Redont, and A. Soubeyran, Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-??ojasiewicz Inequality, Mathematics of Operations Research, vol.35, issue.2, pp.438-457, 2010.
DOI : 10.1287/moor.1100.0449

H. Attouch, J. Bolte, and B. F. Svaiter, Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward???backward splitting, and regularized Gauss???Seidel methods, Mathematical Programming, vol.31, issue.1, pp.91-129, 2011.
DOI : 10.1007/s10107-011-0484-9

URL : https://hal.archives-ouvertes.fr/inria-00636457

A. Auslender, Asymptotic properties of the fenchel dual functional and applications to decomposition problems, Journal of Optimization Theory and Applications, vol.14, issue.3, pp.427-449, 1992.
DOI : 10.1007/BF00940050

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, issue.7, pp.1334-1345, 2002.
DOI : 10.1364/JOSAA.19.001334

H. H. Bauschke, P. L. Combettes, and D. R. Luke, A new generation of iterative transform algorithms for phase contrast tomography, Proc. Int. Conf. Acoust., Speech Signal Process. (ICASSP 2005), pp.89-92, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00017775

H. H. Bauschke, P. L. Combettes, and D. Noll, Joint minimization with alternating Bregman proximity operators, Pac. J. Optim, vol.2, issue.3, pp.401-424, 2006.

J. Bolte, A. Daniilidis, and A. Lewis, The ??ojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems, SIAM Journal on Optimization, vol.17, issue.4, pp.1205-1223, 2006.
DOI : 10.1137/050644641

J. Bolte, A. Daniilidis, A. Lewis, and M. Shiota, Clarke Subgradients of Stratifiable Functions, SIAM Journal on Optimization, vol.18, issue.2, pp.556-572, 2007.
DOI : 10.1137/060670080

J. Bolte, A. Daniilidis, O. Ley, and L. Mazet, Characterizations of ??ojasiewicz inequalities: Subgradient flows, talweg, convexity, Transactions of the American Mathematical Society, vol.362, issue.06, pp.3319-3363, 2010.
DOI : 10.1090/S0002-9947-09-05048-X

J. Bolte, S. Sabach, and M. Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems, Mathematical Programming, vol.4, issue.1-2, 2013.
DOI : 10.1007/s10107-013-0701-9

URL : https://hal.archives-ouvertes.fr/hal-00916090

L. M. Brègman, The method of successive projection for finding a common point of convex sets, Soviet Math. Dokl, vol.6, issue.688, p.692, 1965.

E. Candès, Y. Eldar, T. Strohmer, and V. Voroninski, Phase Retrieval via Matrix Completion, SIAM Journal on Imaging Sciences, vol.6, issue.1, pp.199-225, 2013.
DOI : 10.1137/110848074

Y. Censor and A. Lent, Optimization of ???$\log x$??? Entropy over Linear Equality Constraints, SIAM Journal on Control and Optimization, vol.25, issue.4, pp.921-933, 1987.
DOI : 10.1137/0325050

E. Chouzenoux, J. C. Pesquet, and A. Repetti, Variable Metric Forward???Backward Algorithm for Minimizing the Sum of a Differentiable Function and a Convex Function, Journal of Optimization Theory and Applications, vol.21, issue.2, pp.10957-10970, 2013.
DOI : 10.1007/s10957-013-0465-7

URL : https://hal.archives-ouvertes.fr/hal-00789970

P. L. Combettes, J. C. Pesquet, R. Bauschke, P. L. Burachik, V. Combettes et al., Proximal Splitting Methods in Signal Processing, Fixed- Point Algorithms for Inverse Problems in Science and Engineering, pp.185-212, 2010.
DOI : 10.1007/978-1-4419-9569-8_10

URL : https://hal.archives-ouvertes.fr/hal-00643807

P. L. Combettes and B. C. V?uv?u, Variable metric quasi-Fejér monotonicity. Nonlinear Anal, pp.17-31, 2013.
DOI : 10.1016/j.na.2012.09.008

URL : http://arxiv.org/abs/1206.5705

P. L. Combettes and V. R. Wajs, Signal Recovery by Proximal Forward-Backward Splitting, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1168-1200, 2005.
DOI : 10.1137/050626090

URL : https://hal.archives-ouvertes.fr/hal-00017649

J. C. Dainty and J. R. Fienup, Phase retrieval and image reconstruction for astronomy, Image Recovery: Theory and Application, pp.231-275, 1987.

J. A. Fessler, Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction, IEEE Transactions on Medical Imaging, vol.16, issue.2, pp.166-175, 1997.
DOI : 10.1109/42.563662

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

J. R. Fienup, Phase retrieval algorithms: a comparison, Applied Optics, vol.21, issue.15, pp.2758-2769, 1982.
DOI : 10.1364/AO.21.002758

R. W. Gerchberg and W. O. Saxton, A practical algorithm for the determination of phase from image and diffraction plane pictures, Optik, vol.35, pp.237-246, 1972.

J. B. Hiriart-urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms, 1993.
DOI : 10.1007/978-3-662-02796-7

M. W. Jacobson and J. A. Fessler, An Expanded Theoretical Treatment of Iteration-Dependent Majorize-Minimize Algorithms, IEEE Transactions on Image Processing, vol.16, issue.10, pp.2411-2422, 2007.
DOI : 10.1109/TIP.2007.904387

K. Kurdyka and A. Parusinski, w f -stratification of subanalytic functions and the Lojasiewicz inequality Comptes rendus de l'Académie des sciences Série 1, Une propriété topologique des sous-ensembles analytiques réels Editions du centre National de la Recherche Scientifique, pp.129-133, 1963.

D. G. Luenberger, Linear and Nonlinear Programming, 1973.
DOI : 10.1007/978-3-319-18842-3

Z. Q. Luo and P. Tseng, On the convergence of the coordinate descent method for convex differentiable minimization, Journal of Optimization Theory and Applications, vol.34, issue.B, pp.7-35, 1992.
DOI : 10.1007/BF00939948

Z. Q. Luo and P. Tseng, On the Linear Convergence of Descent Methods for Convex Essentially Smooth Minimization, SIAM Journal on Control and Optimization, vol.30, issue.2, pp.408-425, 1992.
DOI : 10.1137/0330025

S. Mallat, A Wavelet Tour of Signal Processing, 2009.

B. S. Mordukhovich, Basic theory, Series of, Variational Analysis and Generalized Differentiation. Comprehensive Studies in Mathematics, vol.330, 2006.

J. J. Moreau, Proximit?? et dualit?? dans un espace hilbertien, Bulletin de la Société mathématique de France, vol.79, pp.273-299, 1965.
DOI : 10.24033/bsmf.1625

URL : http://archive.numdam.org/article/BSMF_1965__93__273_0.pdf

P. Ochs, Y. Chen, T. Brox, and T. Pock, iPiano: Inertial Proximal Algorithm for Nonconvex Optimization, SIAM Journal on Imaging Sciences, vol.7, issue.2, 2013.
DOI : 10.1137/130942954

URL : http://arxiv.org/abs/1404.4805

J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, 1970.
DOI : 10.1137/1.9780898719468

M. J. Powell, On search directions for minimization algorithms, Mathematical Programming, vol.3, issue.1, pp.193-201, 1973.
DOI : 10.1007/BF01584660

M. Razaviyayn, M. Hong, and Z. Luo, A Unified Convergence Analysis of Block Successive Minimization Methods for Nonsmooth Optimization, SIAM Journal on Optimization, vol.23, issue.2, pp.1126-1153, 2013.
DOI : 10.1137/120891009

P. Richtárik and M. Talác, Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function, Mathematical Programming, vol.67, issue.1, pp.1-38, 2012.
DOI : 10.1007/s10107-012-0614-z

P. Richtárik and M. Talác, Inexact coordinate descent: complexity and preconditioning, Tech. rep, 2013.

S. Saquib, J. Zheng, C. A. Bouman, and K. D. Sauer, Parallel computation of sequential pixel updates in statistical tomographic reconstruction, Proc. IEEE Int. Conf. Image Processing, pp.93-96, 1995.

S. Sotthivirat and J. A. Fessler, Image recovery using partitioned-separable paraboloidal surrogate coordinate ascent algorithms, IEEE Transactions on Image Processing, vol.11, issue.3, pp.306-317, 2002.
DOI : 10.1109/83.988963

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

P. Tseng, Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization, Journal of Optimization Theory and Applications, vol.109, issue.3, pp.475-494, 2001.
DOI : 10.1023/A:1017501703105

I. Waldspurger, A. Aspremont, and S. Mallat, Phase recovery, MaxCut and complex semidefinite programming, Mathematical Programming, vol.16, issue.3, 2013.
DOI : 10.1007/s10107-013-0738-9

URL : https://hal.archives-ouvertes.fr/hal-00907535

Y. Xu and W. Yin, A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion, SIAM Journal on Imaging Sciences, vol.6, issue.3, pp.1758-1789, 2013.
DOI : 10.1137/120887795

W. I. Zangwill, Nonlinear Programming, 1969.