M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, 2010.

D. Donoho, Compressed sensing, IEEE Transactions on Information Theory, vol.52, issue.4, pp.1289-1306, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00369486

I. Daubechies, M. Defrise, and C. De-mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, vol.57, issue.11, pp.1413-1457, 2004.

M. Elad, M. Figueiredo, and Y. Ma, On the role of sparse and redundant representations in image processing, Proceedings of the IEEE, vol.98, issue.6, pp.972-982, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00568893

F. Marvasti, A. Amini, F. Haddadi, M. Soltanolkotabi, B. Khalaj et al., A unified approach to sparse signal processing, EURASIP Journal on Advances in Signal Processing, vol.2012, issue.1, p.44, 2012.

R. Baraniuk, M. Davenport, R. Devore, and M. Wakin, A simple proof of the restricted isometry property for random matrices, Constructive Approximation, vol.28, issue.3, pp.253-263, 2008.

N. Ahmed, T. Natarajan, and K. Rao, Discrete cosine transform, IEEE Transactions on Computers, vol.100, issue.1, pp.90-93, 1974.

I. Daubechies, Orthonormal bases of compactly supported wavelets, Communications on Pure and Applied Mathematics, vol.41, issue.7, pp.909-996, 1988.

I. Tosic and P. Frossard, Dictionary learning: What is the right representation for my signal?, IEEE Signal Processing Magazine, vol.28, pp.27-38, 2011.

M. Unser and P. D. Tafti, An Introduction to Sparse Stochastic Processes, vol.367, 2014.

A. Amini and M. Unser, Sparsity and infinite divisibility, IEEE Transactions on Information Theory, vol.60, issue.4, pp.2346-2358, 2014.

A. Amini, M. Unser, and F. Marvasti, Compressibility of deterministic and random infinite sequences, IEEE Transactions on Signal Processing, vol.59, issue.11, pp.5193-5201, 2011.

G. Tzagkarakis, P. John, P. Nolan, and . Tsakalides, Compressive sensing using symmetric alpha-stable distributions for robust sparse signal reconstruction, IEEE Transactions on Signal Processing, vol.67, issue.3, pp.808-820, 2018.

N. Bassiou, C. Kotropoulos, and E. Koliopoulou, Symmetric ?-stable sparse linear regression for musical audio denoising, 2013 8th International Symposium on Image and Signal Processing and Analysis (ISPA), pp.382-387, 2013.

J. Nolan, Stable Distributions: Models for Heavy-Tailed Data, 2003.

C. L. Nikias and M. Shao, Signal Processing with Alpha-Stable Distributions and Applications, 1995.

P. Pad, F. Salehi, E. Celis, P. Thiran, and M. Unser, Dictionary learning based on sparse distribution tomography, Proceedings of the Thirty-Fourth International Conference on Machine Learning (ICML'17), pp.2731-2740, 2017.

G. Samoradnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, vol.632, 2017.

J. Mockus and L. Mockus, Bayesian approach to global optimization and application to multiobjective and constrained problems, Journal of Optimization Theory and Applications, vol.70, issue.1, pp.157-172, 1991.