Reconstruction of wavelet coefficients using total variation minimization

SIAM Journal on Scientific Computing

Volumn 24, Issue 5, 2003, Pages 1754-1767

  Durand, Sylvain ^a,b   Froment, Jacques ^b,c  

^a Faculté de Mathématiques et d Informatique   (France)

^b Inserm   (France)

^c UNIVERSITÉ DE BRETAGNE SUD   (France)

Author keywords

Denoising; Subgradient method; Total variation; Wavelet

Indexed keywords

COMPUTER SIMULATION; ESTIMATION; IMAGE ENHANCEMENT; IMAGE RECONSTRUCTION; PIECEWISE LINEAR TECHNIQUES; SPURIOUS SIGNAL NOISE; WAVELET TRANSFORMS;

PSEUDO-GIBBS ARTIFACTS; SUBGRADIENT METHOD; TOTAL VARIATION MINIMIZATION; WAVELET COEFFICIENTS; WAVELET SIGNAL DENOISING METHODS;

ALGORITHMS;

EID: 0141975226     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827501397792     Document Type: Article

References (25)

1. R. Acar and C.R. Vogel, Analysis of total variation penalty methods for ill-posed problems, Inverse Problems, 10 (1994), pp. 1217-1229.
2. Y. Bobichon and A. Bijaoui, Regularized multiresolution methods for astronomical image enhancement, Exper. Astron., 7 (1997), pp. 239-255.
3. A. Chambolle and P.-L. Lions, Image recovery via total variation minimization and related problems, Numer. Math., 76 (1997), pp. 167-188.
4. T.-F. Chan, H.M. Zhou, and R.H. Chan, A Continuation Method for Total Variation Denoising Problems, UCLA CAM Report 95-18, University of California, Los Angeles, CA, 1995.
5. T. Chan, A. Marquina, and P. Mulet, High-order total variation-based image restoration, SIAM J. Sci. Comput., 22 (2000), pp. 503-516.
6. T.F. Chan and H.M. Zhou, Total variation improved wavelet thresholding in image compression, in Proceedings of the 2000 International Conference on Image Processing, Vol. 2, IEEE Press, Piscataway, NJ, 2000, pp. 391-394.
7. A. Cohen and J.-P. D'Ales, Nonlinear approximation of random functions, SIAM J. Appl. Math., 57 (1997), pp. 518-540.
8. A. Cohen, I. Daubechies, and P. Vial, Wavelets and fast wavelet transforms on an interval, Appl. Comput. Harmon. Anal., 1 (1993), pp. 54-81.
9. A. Cohen, J. Froment, and J. Istas, Analyse multiréresolution des signaux aléatoires, C. R. Acad. Sci. Paris Sér. I Math, 312 (1991), pp. 567-570.
10. R.R. Coifman and D.L. Donoho, Translation-invariant de-noising, in Wavelets and Statistics, A. Antoniadis and G. Oppenheim, eds., Springer-Verlag, 1995, pp. 125-150.
11. R.R. Coifman and A. Sowa, Combining the calculus of variations and wavelets for image enhancement, Appl. Comput. Harmon. Anal., 9 (2000), pp. 1-18.
12. D.C. Dobson and F. Santosa, Recovery of blocky images from noisy and blurred data, SIAM J. Appl. Math., 56 (1996), pp. 1181-1198.
13. D.C. Dobson and C.R. Vogel, Convergence of an iterative method for total variation denoising, SIAM J. Numer. Anal., 34 (1997), pp. 1779-1791.
14. D. Donoho, De-noising by soft-thresholding, IEEE Trans. Inform. Theory, 41 (1995), pp. 613-627.
15. D. Donoho and I. Johnstone, Ideal spatial adaptation via wavelet shrinkage, Biometrika, 81 (1994), pp. 425-455.
16. S. Durand and J. Froment, Artifact free signal denoising with wavelets, in Proceedings of the 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol. 6, IEEE Press, Piscataway, NJ, 2001, pp. 3685-3688.
17. S. Durand, F. Malgouyres, and B. Rougé, Image deblurring, spectrum interpolation and application to satellite imaging, ESAIM. Control Optim. Cal. Var., 5 (2000), pp. 445-475.
18. J. Froment and L. Moisan, eds., MegaWave2 v.2.10, http://www.cmla.ens-cachan.fr/Cmla/Megawave/index.html (17 December 2002).
19. F. Malgouyres, Combining total variation and wavelet packet approaches for image deblurring, in Proceedings of the IEEE Workshop on Variational and Level Set Methods, IEEE Press, Piscataway, NJ, 2001, pp. 57-64.
20. S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, San Diego, CA, 1997.
21. L. Moisan, Extrapolation de spectre et variation totale pondérée, in Proceedings of the 12th Symposium GRETSI'01 on Signal and Image Processing, Toulouse, France, 2001.
22. M. Nikolova, Local strong homogeneity of a regularized estimator, SIAM J. Appl. Math., 61 (2000), pp. 633-658.
23. L.I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259-268.
24. N.Z. Shor, Minimization Methods for Non-Differentiable Functions, Springer-Verlag, Berlin, 1985.
25. C.R. Vogel and M.E. Oman, Iterative method for total variation denoising, SIAM J. Sci. Comput., 17 (1996), pp. 227-238.