Sparsity and persistence: mixed norms provide simple signal models with dependent coefficients

作者: Matthieu Kowalski , Bruno Torrésani

DOI: 10.1007/S11760-008-0076-1

关键词: MathematicsAlgorithmPrior probabilityApplied mathematicsMorphological component analysisRelaxation algorithmMixed normBasis pursuit denoisingNorm (mathematics)Noise reductionSparse approximation

摘要: … , and propose alternatives that overcome some potential shortcomings in specific situations. To this end, we applied G-LASSO and E-LASSO and variants to simulated signals, …

参考文章(24)
Ronald R. Coifman, Maxim J. Goldberg, Jonathan Berger, Removing noise from music using local trigonometric bases and wavelet packets Journal of The Audio Engineering Society. ,vol. 42, pp. 808- 818 ,(1994)
Joel A. Tropp, Anna C. Gilbert, Martin J. Strauss, Algorithms for simultaneous sparse approximation: part I: Greedy pursuit Signal Processing. ,vol. 86, pp. 572- 588 ,(2006) , 10.1016/J.SIGPRO.2005.05.030
L. DAUDET, S. MOLLA, B. TORRESANI, TOWARDS A HYBRID AUDIO CODER Proceedings of the International Computer Congress 2004. ,vol. 1, pp. 13- 24 ,(2004) , 10.1142/9789812702654_0002
Scott Shaobing Chen, David L. Donoho, Michael A. Saunders, Atomic Decomposition by Basis Pursuit SIAM Journal on Scientific Computing. ,vol. 20, pp. 33- 61 ,(1998) , 10.1137/S1064827596304010
R. Gribonval, M. Nielsen, Sparse approximations in signal and image processing Signal Processing. ,vol. 86, pp. 415- 416 ,(2006) , 10.1016/J.SIGPRO.2005.07.012
M. Elad, J.-L. Starck, P. Querre, D.L. Donoho, Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA) Applied and Computational Harmonic Analysis. ,vol. 19, pp. 340- 358 ,(2005) , 10.1016/J.ACHA.2005.03.005
L. Daudet, B. Torrésani, Hybrid representations for audiophonic signal encoding Signal Processing. ,vol. 82, pp. 1595- 1617 ,(2002) , 10.1016/S0165-1684(02)00304-3
Paul Tseng, Dual coordinate ascent methods for non-strictly convex minimization Mathematical Programming. ,vol. 59, pp. 231- 247 ,(1993) , 10.1007/BF01581245
Massimo Fornasier, Holger Rauhut, Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints SIAM Journal on Numerical Analysis. ,vol. 46, pp. 577- 613 ,(2008) , 10.1137/0606668909
Matthieu Kowalski, Sparse regression using mixed norms Applied and Computational Harmonic Analysis. ,vol. 27, pp. 303- 324 ,(2009) , 10.1016/J.ACHA.2009.05.006