Multidimensional shrinkage-thresholding operator and group LASSO penalties

IEEE Signal Processing Letters

Volumn 18, Issue 6, 2011, Pages 363-366

  Puig, Arnau Tibau ^a,b   Wiesel, Ami ^c   Fleury, Gilles ^b   Hero, Alfred O ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

^b SUPELEC   (France)

^c HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

group LASSO regression; proximity operator; Shrinkage thresholding operator

Indexed keywords

CONVEX OPTIMIZATION; DIGITAL IMAGE STORAGE; IMAGE COMPRESSION; NUMBER THEORY; QUADRATIC PROGRAMMING; REGRESSION ANALYSIS;

CONVEX OPTIMIZATION PROBLEMS; GENE MICROARRAY DATUM; GROUP LASSOS; JPEG2000 IMAGE COMPRESSION; PROXIMITY OPERATOR; QUADRATIC OPTIMIZATION; THRESHOLDING OPERATORS; VARIABLE SELECTION ALGORITHMS;

SHRINKAGE;

EID: 79955502711     PISSN: 10709908     EISSN: None     Source Type: Journal    
DOI: 10.1109/LSP.2011.2139204     Document Type: Article

References (19)

1. I. Daubechies, M. Defrise, and C. de Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint", Commun. Pure Appl. Math., vol. 57, no. 11, pp. 1413-1457, 2004. (Pubitemid 39427442)
2. A. Beck and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems", SIAM J. Imag. Sci., vol. 2, pp. 183-202, 2009.
3. R. D. Nowak and M. A. T. Figueiredo, "Fast wavelet-based image deconvolution using the EM algorithm", in Conf. Rec. 35th Asilomar Conf., 2001, vol. 1.
4. R. Tibshirani, T. Hastie, B. Narasimhan, and G. Chu, "Class prediction by nearest shrunken centroids, with applications to DNA microarrays", Statist. Sci., pp. 104-117, 2003. (Pubitemid 41461824)
5. J. A. Bazerque, G. Mateos, and G. B. Giannakis, "Group-lasso on splines for spectrumcartography", Arxiv Preprint arXiv:1010.0274 2010.
6. M. B. Wakin, M. F. Duarte, S. Sarvotham, D. Baron, and R. G. Baraniuk, "Recovery of jointly sparse signals from few random projections", in Proc. Neural Inform. Processing Systems-NIPS, 2005.
7. M. Yuan and Y. Lin, "Model selection and estimation in regression with grouped variables", J. Royal Statist. Soc. B, vol. 68, pp. 49-67, 2006. (Pubitemid 43415335)
8. D. Malioutov, M. Cetin, and A. S. Willsky, "A sparse signal reconstruction perspective for source localizationwith sensor arrays", IEEE Trans. Signal Processing, vol. 53, no. 8, pt. 2, pp. 3010-3022, Aug. 2005. (Pubitemid 41372811)
9. P. Zhao, G. Rocha, and B. Yu, "The composite absolute penalties family for grouped and hierarchical variable selection", Ann. Statist., vol. 37, no. 6 A, pp. 3468-3497, 2009.
10. R. Jenatton, J. Mairal, G. Obozinski, and F. Bach, "Proximal methods for sparse hierarchical dictionary learning", in Proc. 27th Int. Conf. Machine Learning, 2010.
11. P. L. Combettes and V. R. Wajs, "Signal recovery by proximal forwardbackward splitting", Multiscale Model. Simul., vol. 4, no. 4, pp. 1168-1200, 2006.
12. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U. K.: Cambridge Univ. Press.
13. M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, "Applications of second-order cone programming", Linear Algebra Applicat., vol. 284, no. 1-3, pp. 193-228, 1998.
14. S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, "Sparse reconstruction by separable approximation", IEEE Trans. Signal Process., vol. 57, no. 7, pp. 2479-2493, July 2009.
15. J. C. Dunn, "Newton's method and the Goldstein step-length rule for constrained minimization problems", SIAM J. Contr. Optim., vol. 18, p. 659, 1980.
16. L. el Ghaoui and H. Lebret, "Robust solutions to least squares problems with uncertain data", SIAM J. Matrix Anal. Applicat., Oct. 1997.
17. P. Tseng, "Convergence of a block coordinate descent method for nondifferentiable minimization", J. Optim. Theory Applicat., vol. 109, no. 3, pp. 475-494, 2001.
18. J. J. Moreau, "Proximité et dualité dans un espace hilbertien", Bull. Soc. Math. France, vol. 93, no. 2, pp. 273-299, 1965.
19. P. Sprechmann, I. Ramirez, G. Sapiro, and Y. Eldar, "Collaborative hierarchical sparse modeling", in 44th Annual IEEE Conf. Information Sciences and Systems (CISS), 2010, 2010, pp. 1-6.