Universal priors for sparse modeling

CAMSAP 2009 - 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing

Volumn , Issue , 2009, Pages 197-200

  Raḿrez, Ignacio ^a   Lecumberry, Federico ^b   Sapiro, Guillermo ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

^b UNIVERSIDAD DE LA REPÚBLICA   (Uruguay)

Author keywords

[No Author keywords available]

Indexed keywords

CODING PERFORMANCE; GRAM MATRICES; LINEAR COMBINATIONS; MUTUAL COHERENCE; SIGNAL AND IMAGE PROCESSING; SPARSE DATA;

IMAGE PROCESSING; INFORMATION THEORY; TECHNICAL PRESENTATIONS;

SENSORS;

EID: 77951108336     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CAMSAP.2009.5413302     Document Type: Conference Paper

References (25)

1. M. Aharon, M. Elad, and A. Bruckstein. The K-SVD: An algorithm for designing of overcomplete dictionaries for sparse representations. IEEE Trans. SP, 54(11):4311-4322, Nov. 2006.
2. A. Barron, J. Rissanen, and B. Yu. The minimum description length principle in coding and modeling. IEEE Trans. IT, 44(6):2743-2760, 1998.
3. A. M. Bruckstein, D. L. Donoho, and M. Elad. From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Review, 51(1):34-81, Feb. 2009.
4. E. J. Candès, J. K. Romberg, and T. Tao. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. IT, 52(2):489-509, 2006.
5. 1 minimization. J. Fourier Anal. Appl., 14(5):877-905, Dec. 2008.
6. S. Chen, D. Donoho, and M. Saunders. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 20(1):33-61, 1998.
7. Thomas M. Cover and Joy A. Thomas. Elements of information theory. John Wiley and Sons, Inc., 2 edition, 2006.
8. I. Daubechies, M. Defrise, and C. De Mol. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Comm. on Pure and Applied Mathematics, 57:1413-1457, 2004.
9. B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani. Least angle regression. Annals of Statistics, 32(2):407-499, 2004.
10. M. Elad. Optimized projections for compressed-sensing. IEEE Trans. SP, 55(12):5695-5702, Dec. 2007.
11. M. Elad and M. Aharon. Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. IP, 54(12):3736-3745, Dec. 2006.
12. K. Engan, S. O. Aase, and J. H. Husoy. Multi-frame compression: Theory and design. Signal Processing, 80(10):2121-2140, Oct. 2000.
13. J. Fan and R. Li. Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Stat. Assoc., 96(456):1348-1360, Dec. 2001.
14. M. A. T. Figueiredo. Adaptive sparseness using Jeffreys prior. In Thomas G. Dietterich, Suzanna Becker, and Zoubin Ghahramani, editors, Adv. NIPS, pages 697-704. MIT Press, 2001.
15. R. Giryes, Y. C. Eldar, and M. Elad. Automatic parameter setting for iterative shrinkage methods. In IEEE 25-th Convention of Electronics and Electrical Engineers in Israel (IEEEI'08), Dec. 2008.
16. B. Krishnapuram, L. Carin, M. A. T. Figueiredo, and A. J. Hartemink. Sparse multinomial logistic regression: Fast algorithms and generalization bounds. IEEE Trans. PAMI, 27(6):957-968, 2005.
17. J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman. Supervised dictionary learning. In D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou, editors, Adv. NIPS, volume 21, 2009.
18. J. Mairal, M. Elad, and G. Sapiro. Sparse representation for color image restoration. IEEE Trans. IP, 17(1):53-69, Jan. 2008.
19. S. Mallat and Z. Zhang. Matching pursuit in a time-frequency dictionary. IEEE Trans. SP, 41(12):3397-3415, 1993.
20. B. Olshausen and D. Field. Sparse coding with an overcomplete basis set: A strategy employed by V1? Vision Research, 37:3311-3325, 1997.
21. I. Ramirez, F. Lecumberry, and G. Sapiro. Universal priors for sparse signal modeling: Marrying information theory with sparse coding. IMA Preprint, http://www.ima.umn.edu/preprints/aug2009/2279.pdf, 2009.
22. M. E. Tipping. Sparse bayesian learning and the relevance vector machine. Journal of Machine Learning Research, 1:211-244, 2001.
23. J. A. Tropp. Greed is good: Algorithmic results for sparse approximation. IEEE Trans. IT, 50(10):2231-2242, Oct. 2004.
24. H. Zou. The adaptive LASSO and its oracle properties. J. Am. Stat. Assoc., 101:1418-1429, 2006.
25. H. Zou and R. Li. One-step sparse estimates in nonconcave penalized likelihood models. Annals of Statistics, 36(4):1509-1533, 2008.