Stein block thresholding for wavelet-based image deconvolution

Electronic Journal of Statistics

Volumn 4, Issue , 2010, Pages 415-435

  Chesneau, Christophe ^a   Fadili, Jalal ^a   Starck, Jean Luc ^b  

^a UNIVERSITÉ DE CAEN   (France)

^b UNIVERSITÉ PARIS DIDEROT   (France)

Author keywords

Block thresholding; Image deconvolution; LATEX 2 ; Minimax; Wavelets

Indexed keywords

EID: 80055030541     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-EJS550     Document Type: Article

References (21)

1. F. Abramovich and B. W. Silverman. Wavelet decomposition approaches to statistical inverse problems. Biometrika, 85:115–129, 1998.
2. R. J. Adler. An introduction to continuity, extrema, and related topics for general Gaussian processes. Institute of Mathematical Statistics, Hayward, CA, 1990.
3. T. Cai. On adaptive wavelet estimation of a derivative and other related linear inverse problems. J. Statistical Planning and Inference, 108:329–349, 2002.
4. C. Chaux, P. L. Combettes, J.-C. Pesquet, and V. R. Wajs. A variational formulation for frame-based inverse problems. Inv. Prob., 23:1495–1518, 2007.
5. p risk. Statistica Sinica, 18(3):1007–1024, 2008.
6. C. Chesneau, M. J. Fadili, and J.-L. Starck. Stein block thresholding for image denoising. Applied and Computational Harmonic Analysis, 28(1):67–88, 2010.
7. I. Daubechies, M. Defrise, and C. De Mol. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Comm. Pure Appl. Math., 57:1413–1541, 2004.
8. R. Devore, G. Kerkyacharian, D. Picard, and V. Temlyakov. On mathematical methods of learning. Foundations of Computational Mathematics, 1:3–58, 2006.
9. D. Donoho and M. Raimondo. A fast wavelet algorithm for image deblurring. The Australian & New Zealand Industrial and Applied Mathematics Journal, 46:C29–C46, 2005.
10. D.L. Donoho. Nonlinear solution of inverse problems by waveletvaguelette decomposition. Applied and Computational Harmonic Analysis, 2:101–126, 1995.
11. M. J. Fadili and J.-L. Starck. Sparse representation-based image deconvolution by iterative thresholding. In ADA 4, France, 2006. Elsevier.
12. M. Figueiredo and R. Nowak. An EM algorithm for wavelet-based image restoration. ITIP, 12(8):906–916, 2003.
13. I.M. Johnstone, G. Kerkyacharian, D. Picard, and M. Raimondo. Wavelet deconvolution in a periodic setting. Journal of the Royal Statistical Society. Series B. Methodological, 66:547–573, 2004.
14. J. Kalifa, S. Mallat, and B. Rougé. Image deconvolution in mirror wavelet bases. In IEEE ICIP, volume 1, pages 565–569, 1998.
15. S. Mallat. A wavelet tour of signal processing. Academic Press, 2nd edition, 1998.
16. Y. Meyer. Wavelet and Operators. Cambridge University Press, 1992.
17. R. Neelamani, H. Choi, and R. Baraniuk. Forward: Fourier-wavelet regularized deconvolution for ill-conditioned systems. IEEE Transactions on signal processing, 52:418–433, 2004.
18. J.-C. Pesquet, A. Benazza-Benyahia, and C. Chaux. A sure approach for digital signal/image deconvolution problems. IEEE Transactions on Image Processing, 57(12):4616–4632, 2009.
19. A.B. Tsybakov. Introduction à l’estimation nonparametrique. Springer, New York, 2004.
20. C. Vonesh, S. Ramani, and M. Unser. Recursive risk estimation for non-linear image deconvolution with a wavelet-domain sparsity constraint. In IEEE International Conference on Image Processing, ICIP’08, pages 665–668, San Diego, CA, October 2008.
21. Wavelab 802. Wavelab toolbox. http://www-stat.stanford.edu/˜wavelab, 2001.