, Nonlinear Programming: Theory and Algorithms, 1979.
DOI : 10.1002/0471787779
, The space $L\sp{p}$ , with mixed norm, Duke Mathematical Journal, vol.28, issue.3, pp.301-324, 1961.
DOI : 10.1215/S0012-7094-61-02828-9
, Removing noise from music using local trigonometric bases and wavelet packets, J. Audio Eng. Soc, vol.42, issue.10, pp.808-818, 1994.
, Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage, IEEE Transactions on Image Processing, vol.7, issue.3, pp.320-353, 1998.
DOI : 10.1109/83.661182
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.4107
, 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
, On the importance of combining wavelet-based nonlinear approximation with coding strategies, IEEE Transactions on Information Theory, vol.48, issue.7, pp.1895-1921, 2002.
DOI : 10.1109/TIT.2002.1013132
, 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
, Sparse solutions to linear inverse problems with multiple measurement vectors, IEEE Transactions on Signal Processing, vol.53, issue.7, pp.2477-2488, 2005.
DOI : 10.1109/TSP.2005.849172
, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Communications on Pure and Applied Mathematics, vol.58, issue.11, pp.1413-1457, 2004.
DOI : 10.1002/cpa.20042
, TOWARDS A HYBRID AUDIO CODER, Wavelet Analysis and Its Applications, and Active Media Technology, pp.13-24, 2004.
DOI : 10.1142/9789812702654_0002
URL : https://hal.archives-ouvertes.fr/hal-01304850
, Hybrid representations for audiophonic signal encoding, special issue on Image and Video Coding Beyond Standards, pp.1595-1617, 2002.
DOI : 10.1016/S0165-1684(02)00304-3
URL : https://hal.archives-ouvertes.fr/hal-01300317
, Modulation spaces: Looking back and ahead, Sampling Theory in Signal and, Image Processing, vol.5, issue.3, pp.109-140, 2006.
, Sparse Regression with Structured Priors: Application to Audio Denoising, 2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings, 2006.
DOI : 10.1109/ICASSP.2006.1660589
, Iterative thresholding algorithms, Applied and Computational Harmonic Analysis, vol.25, issue.2, pp.187-208, 2008.
DOI : 10.1016/j.acha.2007.10.005
URL : http://doi.org/10.1016/j.acha.2007.10.005
, Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints, SIAM Journal on Numerical Analysis, vol.46, issue.2, pp.577-613, 2008.
DOI : 10.1137/0606668909
, Nonlinear Approximation with Local Fourier Bases, Constructive Approximation, vol.16, issue.3, pp.317-331, 2000.
DOI : 10.1007/s003659910014
, Random Models for Sparse Signals Expansion on Unions of Bases With Application to Audio Signals, IEEE Transactions on Signal Processing, vol.56, issue.8, pp.3468-3481, 2008.
DOI : 10.1109/TSP.2008.920144
URL : https://hal.archives-ouvertes.fr/hal-00142088
, Sparsity and persistence: mixed norms provide simple signals models with dependent coefficients, Signal, Image and Video Processing doi:10, pp.11760-11768, 1007.
, Under-determined source separation via mixed-norm regularized minimization, Proceedings of the European Signal Processing Conference
URL : https://hal.archives-ouvertes.fr/hal-00347089
, On the existence and nonexistence of Lagrange multipliers in Banach spaces, Journal of Optimization Theory and Applications, vol.17, issue.1, pp.81-110, 1976.
DOI : 10.1007/BF00933349
, A wavelet tour of signal processing, 1998.
, Proximit et dualit dans un espace hilbertien, Bull. Soc. Math. France, vol.93, pp.273-299, 1965.
, Subset selection in noise based on diversity measure minimization, IEEE Transactions on Signal Processing, vol.51, issue.3, pp.760-770, 2003.
DOI : 10.1109/TSP.2002.808076
, An affine scaling methodology for best basis selection, IEEE Transactions on Signal Processing, vol.47, issue.1, pp.187-200, 1999.
DOI : 10.1109/78.738251
, On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains, Journal of the London Mathematical Society, vol.60, issue.1, pp.237-257, 1999.
DOI : 10.1112/S0024610799007723
, A Shur test for weighted mixed-norm spaces, Analysis Mathematica, pp.31-277, 2005.
, Local Fourier bases and modulation spaces, Turkish Journal of Mathematics, vol.30, issue.4, pp.447-462, 2006.
, Image decomposition via the combination of sparse representations and a variational approach, IEEE Transactions on Image Processing, vol.14, issue.10, pp.1570-1582, 2005.
DOI : 10.1109/TIP.2005.852206
, Morizet-Mahoudeaux, Hierarchical penalization, Advances in Neural Information Processing Systems, 2008.
, Multi-frame representations in linear inverse problems with mixed multi-constraints, Applied and Computational Harmonic Analysis, vol.22, issue.1, pp.43-60, 2006.
DOI : 10.1016/j.acha.2006.05.003
, An iterative algorithm for nonlinear inverse problems with joint sparsity constraints in vector-valued regimes and an application to color image inpainting, Inverse Problems, vol.23, issue.5, pp.1851-1870, 2007.
DOI : 10.1088/0266-5611/23/5/005
, Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society Serie B, vol.58, issue.1, pp.267-288, 1996.
, Model selection and estimation in regression with grouped variables, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.58, issue.1, pp.49-67, 2006.
DOI : 10.1198/016214502753479356
, The composite absolute penalties family for grouped and hierarchical variable selection, The Annals of Statistics
, Regularization and variable selection via the elastic net, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.5, issue.2, pp.301-320, 2005.
DOI : 10.1073/pnas.201162998