M. Aharon, M. Elad, and A. Bruckstein, <tex>$rm K$</tex>-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation, IEEE Transactions on Signal Processing, vol.54, issue.11, pp.4311-4322, 2006.
DOI : 10.1109/TSP.2006.881199

A. Aldroubi, M. Unser, and M. Eden, Cardinal spline filters: Stability and convergence to the ideal sinc interpolator, Signal Processing, vol.28, issue.2, pp.127-138, 1992.
DOI : 10.1016/0165-1684(92)90030-Z

O. Chabiron, F. Malgouyres, J. Tourneret, N. D. Attouch, H. Bolte et al., Proximal alternating minimization and projection methods for nonconvex problems: An approach based on the kurdyka-&#321;ojasiewicz inequality, Math Oper Res, vol.35, issue.2, pp.438-457, 2010.

H. Attouch, J. Bolte, and B. 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, 2013.
DOI : 10.1007/s10107-011-0484-9

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

Y. Bengio and Y. Lecun, Scaling learning algorithms towards ai, Large-Scale Kernel Machines, pp.1-41, 2007.

J. Bolte, S. Sabach, and M. Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems Mathematical Programming, series A pp 1?16, 2013.

J. Cai, J. H. Shen, Z. Ye, and G. , Data-driven tight frame construction and image denoising Applied and Computational Harmonic Analysis To appear Champagnat F, Goussard Y, Idier J (1996) Unsupervised deconvolution of sparse spike trains using stochastic approximation, IEEE Trans Signal Process, vol.44, issue.12, pp.2988-2998, 2013.

S. Chen, D. Donoho, and M. Saunders, Atomic Decomposition by Basis Pursuit, SIAM Journal on Scientific Computing, vol.20, issue.1, pp.33-61, 1998.
DOI : 10.1137/S1064827596304010

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.113.7694

E. Chouzenoux, J. Pesquet, A. Repetti, A. Hal-cohen, and E. Séré, A block coordinate variable metric forwardbackward algorithm Time-frequency localization by non-stationary wavelet packets. in Subband and Wavelet Transforms -Theory and Design An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, pp.571413-1457, 1996.

D. Lathauwer, L. , D. Moor, B. Vandewalle, and J. , ) Approximation of Higher-Order Tensors, SIAM Journal on Matrix Analysis and Applications, vol.21, issue.4, pp.1324-1342, 2000.
DOI : 10.1137/S0895479898346995

P. Delsarte, B. Macq, and D. Slock, Signal adapted multiresolution transform for image coding, IEEE Trans Signal Process, vol.42, issue.11, pp.2955-2966, 1992.

N. Dobigeon and J. Tourneret, Bayesian Orthogonal Component Analysis for Sparse Representation, IEEE Transactions on Signal Processing, vol.58, issue.5, pp.2675-2685, 2010.
DOI : 10.1109/TSP.2010.2041594

URL : https://hal.archives-ouvertes.fr/hal-00548753

J. Duarte-carvajalino and G. Sapiro, Learning to Sense Sparse Signals: Simultaneous Sensing Matrix and Sparsifying Dictionary Optimization, IEEE Transactions on Image Processing, vol.18, issue.7, pp.1395-1408, 2009.
DOI : 10.1109/TIP.2009.2022459

M. Elad, K. Engan, and S. Aase, Sparse and redundant representations: From theory to applications in signal and image processing Method of optimal directions for frame design, Proc. IEEE Int. Conf. Acoust., Speech, and Signal Processing (ICASSP), pp.2443-2446, 1999.
DOI : 10.1007/978-1-4419-7011-4

J. Fadili, J. Starck, M. Elad, and D. Donoho, MCALab: Reproducible Research in Signal and Image Decomposition and Inpainting, Computing in Science & Engineering, vol.12, issue.1, pp.44-62, 2010.
DOI : 10.1109/MCSE.2010.14

URL : https://hal.archives-ouvertes.fr/hal-00806835

G. Grippo and M. Sciandrone, On the convergence of the block nonlinear Gauss???Seidel method under convex constraints, Operations Research Letters, vol.26, issue.3, pp.127-136, 2000.
DOI : 10.1016/S0167-6377(99)00074-7

R. Jenatton, J. Mairal, G. Obozinski, F. Bach, R. Icml-jenatton et al., Proximal methods for sparse hierarchical dictionary learning Proximal methods for hierarchical sparse coding, J Mach Learning Research, vol.12, pp.2297-2334, 2010.

G. Kail, J. Tourneret, N. Dobigeon, and F. Hlawatsch, Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Distance Constraint: A Partially Collapsed Gibbs Sampler Method, IEEE Transactions on Signal Processing, vol.60, issue.6, pp.2727-2743, 2012.
DOI : 10.1109/TSP.2012.2190066

S. Lesage, R. Gribonval, F. Bimbot, and L. Benaroya, Learning Unions of Orthonormal Bases with Thresholded Singular Value Decomposition, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005., pp.293-296, 2005.
DOI : 10.1109/ICASSP.2005.1416298

URL : https://hal.archives-ouvertes.fr/inria-00564483

M. Lewicki and T. Sejnowski, Learning Overcomplete Representations, Neural Computation, vol.33, issue.2, pp.337-365, 2000.
DOI : 10.1109/18.119725

W. Lu and A. Antoniou, Design of digital filters and filter banks by optimization: A state of the art review, Proc. EUSIPCO, pp.351-354, 2000.

Z. 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

B. Macq and J. Mertes, Optimization of linear multiresolution transforms for scene adaptive coding, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.3568-3572, 1993.
DOI : 10.1109/78.258099

B. Mailhé, S. Lesage, R. Gribonval, F. Bimbot, P. Vandergheynst et al., Shift-invariant dictionary learning for sparse representations: extending K-SVD Learning multiscale sparse representations for image and video restoration, Proc. European Signal Process. Conf. (EUSIPCO), pp.214-241, 2008.

J. Mairal, F. Bach, J. Ponce, and G. Sapiro, Online learning for matrix factorization and sparse coding, J Mach Learning Research, vol.11, pp.10-60, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00408716

J. Mairal, F. Bach, and J. Ponce, Task-Driven Dictionary Learning, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.34, issue.4, pp.791-804, 2012.
DOI : 10.1109/TPAMI.2011.156

URL : https://hal.archives-ouvertes.fr/inria-00521534

F. Malgouyres and T. Zeng, A Predual Proximal Point Algorithm Solving a Non Negative Basis Pursuit Denoising Model, International Journal of Computer Vision, vol.14, issue.10, pp.294-311, 2009.
DOI : 10.1007/s11263-009-0227-z

URL : https://hal.archives-ouvertes.fr/hal-00133050

M. Muller, A note on a method for generating points uniformly on n-dimensional spheres, Communications of the ACM, vol.2, issue.4, pp.19-20, 1959.
DOI : 10.1145/377939.377946

B. Olshausen and D. Field, Sparse coding with an overcomplete basis set: A strategy employed by V1?, Vision Research, vol.37, issue.23, pp.3311-3325, 1997.
DOI : 10.1016/S0042-6989(97)00169-7

B. Ophir, M. Lustig, and M. Elad, Multi-Scale Dictionary Learning Using Wavelets, IEEE Journal of Selected Topics in Signal Processing, vol.5, issue.5, pp.1014-1024, 2011.
DOI : 10.1109/JSTSP.2011.2155032

URL : https://hal.archives-ouvertes.fr/hal-00700250

T. Painter and A. Spanias, Perceptual coding of digital audio, Proceedings of the IEEE, vol.88, issue.4, pp.451-515, 2000.
DOI : 10.1109/5.842996

G. Peyré, J. Fadili, and J. Starck, Learning the Morphological Diversity, SIAM Journal on Imaging Sciences, vol.3, issue.3, pp.646-669, 2010.
DOI : 10.1137/090770783

J. Princen and A. Bradley, Analysis/Synthesis filter bank design based on time domain aliasing cancellation, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.34, issue.5, pp.1153-1161, 1986.
DOI : 10.1109/TASSP.1986.1164954

C. Quinsac, N. Dobigeon, A. Basarab, J. Tourneret, and D. Kouamé, Bayesian compressed sensing in ultrasound imaging (2013) A Unified Convergence Analysis of Block Successive Minimization Methods for Nonsmooth Optimization, Proc. of Third International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP11), pp.1126-1153, 2011.

R. Rigamonti, A. Sironi, V. Lepetit, and P. Fua, Learning separable filters Dictionaries for sparse representation, The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Proc IEEE -Special issue on applications of sparse representation and compressive sensing, pp.981045-1057, 2010.

R. Rubinstein, M. Zibulevsky, and M. Elad, Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation, IEEE Transactions on Signal Processing, vol.58, issue.3, pp.1553-1564, 2010.
DOI : 10.1109/TSP.2009.2036477

P. Sallee and B. Olshausen, Learning sparse multiscale image representations Advances in neural information processing systems pp, pp.1327-1334, 2002.

J. Starck, J. Fadili, and F. Murtagh, The Undecimated Wavelet Decomposition and its Reconstruction, IEEE Transactions on Image Processing, vol.16, issue.2, pp.297-309, 2007.
DOI : 10.1109/TIP.2006.887733

URL : https://hal.archives-ouvertes.fr/hal-00080092

J. Thiagarajan, K. Ramamurthy, and A. Spanias, Multilevel dictionary learning for sparse representation of images, 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE), 2011.
DOI : 10.1109/DSP-SPE.2011.5739224