Should penalized least squares regression be interpreted as maximum a posteriori estimation?

IEEE Transactions on Signal Processing

Volumn 59, Issue 5, 2011, Pages 2405-2410

  Gribonval, Rémi ^a,b  

^a INRIA   (France)

^b CAMPUS DE BEAULIEU   (France)

Author keywords

Bayesian methods; maximum a posteriori estimation; mean square error methods; signal denoising

Indexed keywords

A-LAPLACIAN; ADDITIVE WHITE GAUSSIAN NOISE; BAYESIAN; BAYESIAN FRAMEWORKS; BAYESIAN METHODS; DE-NOISING; MAP ESTIMATION; MAP ESTIMATOR; MAXIMUM A POSTERIORI; MAXIMUM A POSTERIORI ESTIMATION; MEAN-SQUARE ERROR METHODS; MINIMUM MEAN-SQUARE ERROR ESTIMATORS; PENALIZED LEAST-SQUARES; PENALTY FUNCTION; QUADRATIC PROGRAMS; SIGNAL DENOISING;

ALGEBRA; BAYESIAN NETWORKS; GAUSSIAN NOISE (ELECTRONIC); INVERSE PROBLEMS; NOISE POLLUTION CONTROL; REGRESSION ANALYSIS; SIGNAL PROCESSING; WHITE NOISE;

ESTIMATION;

EID: 79954564965     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2107908     Document Type: Article

References (13)

1. R. Baraniuk, V. Cevher, and M. Wakin, "Low-dimensional models for dimensionality reduction and signal recovery: A geometric perspective," Proc. IEEE, vol. 98, no. 6, pp. 959-971, Jun. 2010.
2. A. Benazza-Benyahia and J.-C. Pesquet, "Building robust wavelet estimators for multicomponent images using Stein's principle," IEEE Trans. Image Process., vol. 14, no. 11, pp. 1814-1830, Nov. 2005. (Pubitemid 41646074)
3. T. Blu and F. Luisier, "The SURE-LET approach to image denoising," IEEE Trans. Image Process., vol. 16, no. 11, pp. 2778-2786, 2007. (Pubitemid 350141850)
4. P. L. Combettes and J.-C. Pesquet, "Proximal thresholding algorithm for minimization over orthonormal bases," SIAM J. Optim., vol. 18, pp. 1351-1376, 2007.
5. D. Donoho, "Denoising by soft-thresholding," IEEE Trans. Inf. Theory, vol. 41, no. 3, pp. 613-627, May 1995.
6. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, 2006.
7. S. Kay, "Fundamentals of statistical signal processing: Estimation theory," in Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1993.
8. P. Moulin and J. Liu, "Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors," IEEE Trans. Inf. Theory, vol. 45, no. 3, pp. 909-919, Apr. 1999.
9. M. Nikolova, "Model distortions in Bayesian MAP reconstruction, " Inverse Probl. Imag., vol. 1, no. 2, pp. 399-422, 2007.
10. M. Raphan and E. P. Simoncelli, "Learning to be Bayesian without supervision," in Advances in Neural Information Processing Systems (NIPS), B. Schölkopf, J. Platt, and T. Hofmann, Eds. Cambridge, MA: MIT Press, May 2007, vol. 19, pp. 1170-1177.
11. C. Stein, "Estimation of the mean of a multivariate normal distribution," Ann. Statist., vol. 9, no. 6, pp. 1135-1151, 1981.
12. J. S. Turek, I. Yavneh, M. Protter, and M. Elad, "On MMSE and MAP denoising under sparse representation modeling over a unitary dictionary," App. Comput. Harmon. Anal., 2010, Technion University, submitted for publication.
13. H. Zayyani, M. Babaie-Zadeh, and C. Jutten, "Bayesian pursuit algorithm for sparse representation," in Proc. Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Taipei, Taiwan, R.O.C., Apr. 19-24, 2009, pp. 1549-1552.