Dual-augmented lagrangian method for efficient sparse reconstruction

IEEE Signal Processing Letters

Volumn 16, Issue 12, 2009, Pages 1067-1070

  Tomioka, Ryota ^a   Sugiyama, Masashi ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Augmented Lagrangian; L1 regularization; Optimization; Sparse signal reconstruction

Indexed keywords

AUGMENTED LAGRANGIAN; AUGMENTED LAGRANGIAN METHODS; DESIGN MATRIX; DUAL PROBLEM; EFFICIENT ALGORITHM; L1-REGULARIZATION; NUMERICAL COMPARISON; SPARSE RECONSTRUCTION; SPARSE SIGNAL RECONSTRUCTION; STATE-OF-THE-ART ALGORITHMS;

LAGRANGE MULTIPLIERS; REPAIR; SIGNAL ANALYSIS; SIGNAL RECONSTRUCTION;

ALGORITHMS;

EID: 70349600872     PISSN: 10709908     EISSN: None     Source Type: Journal    
DOI: 10.1109/LSP.2009.2030111     Document Type: Article

References (18)

1. R. Tibshirani, "Regression shrinkage and selection via the lasso," J. Roy. Statist. Soc. B, vol. 58, no. 1, pp. 267-288, 1996.
2. S. Chen, D. Donoho, and M. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol. 20, no. 1, pp. 33-61, 1998.
3. I. F. Gorodnitsky and B. D. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Trans. Signal Process., vol. 45, no. 3, pp. 600-616, May 1997.
4. S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, "Sparse solutions to linear inverse problems with multiple measurement vectors," IEEE Trans. Signal Process., vol. 53, no. 7, pp. 2477-2488, Jul. 2005.
5. J. Bioucas-Dias, "Bayesian wavelet-based image deconvolution: A GEM algorithm exploiting a class of heavy-tailed priors," IEEE Trans. Image Process., vol. 15, no. 4, pp. 937-951, Apr. 2006.
6. J. Palmer, D. Wipf, K. Kreutz-Delgado, and B. Rao, "Variational em algorithms for non-Gaussian latent variable models," in Advances in Neural Information Processing Systems 18, Y. Weiss, B. Schölkopf, and J. Platt, Eds. Cambridge, MA: MIT Press, 2006, pp. 1059-1066.
7. M. A. T. Figueiredo, J. M. Bioucas-Dias, and R. D. Nowak, "Majorization-minimization algorithm for wavelet-based image restoration," IEEE Trans. Image Process., vol. 16, no. 12, pp. 2980-2991, Dec. 2007.
8. T. Goldstein and S. Osher, Split Bregman Method for L1 Regularized Problems Dept. Mathematics, UCLA, Los Angeles, Tech. Rep. 08-29, 2008.
9. W. Yin, S. Osher, D. Goldfarb, and J. Darbon, "Bregman iterative algorithms for L1-minimization with applications to compressed sensing," SIAM J. Imag. Sci., vol. 1, no. 1, pp. 143-168, 2008.
10. D. P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods. New York: Academic, 1982.
11. J. Nocedal and S. Wright, Numerical Optimization. Berlin, Germany: Springer, 1999.
12. S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinvesky, "An interior-point method for large-scale l-regularized least squares," IEEE J. Select. Topics Signal Process., vol. 1, no. 4, pp. 606-617, Dec. 2007.
13. M. Figueiredo and R. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process., vol. 12, pp. 906-916, 2003.
14. I. Daubechies, M. Defrise, and C. D. Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math., vol. LVII, pp. 1413-1457, 2004.
15. P. L. Combettes and V. R.Wajs, "Signal recovery by proximal forward-backward splitting," Multiscale Model. and Simul., vol. 4, no. 4, pp. 1168-1200, 2005.
16. S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, "Sparse reconstruction by separable approximation," IEEE Trans. Signal Process., to be published.
17. D. P. Bertsekas, Nonlinear Programming, 2nd ed. Nashua, NH: Athena Scientific, 1999.
18. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.