A fast total variation minimization method for image restoration

Multiscale Modeling and Simulation

Volumn 7, Issue 2, 2008, Pages 774-795

  Huang, Yumei ^a,b   Ng, Michael K ^a   Wen, You Wei ^c,d  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b LANZHOU UNIVERSITY   (China)

^c SOUTH CHINA AGRICULTURAL UNIVERSITY   (China)

^d NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Deblurring; Denoising; Image restoration; Total variation

Indexed keywords

IMAGE RECONSTRUCTION; REPAIR; RESTORATION; WAVELET ANALYSIS;

ALTERNATING MINIMIZATION ALGORITHMS; DE NOISES; DEBLURRING; DENOISING; IMAGE RESTORATION; IMAGE RESTORATIONS; TOTAL VARIATION; TOTAL VARIATION MINIMIZATIONS; TOTAL VARIATIONS;

OPTIMIZATION;

EID: 55149111865     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/070703533     Document Type: Article

References (30)

1. 1-unified variational framework for image restoration, inProceedings of the 8th European Conference on Computer Vision (Prague, 2004), Lecture Notes in Comput. Sci. 3024, Springer, Berlin, 2004, pp.1-13.
2. D. BERTSEKAS, A. NEDIC, and E. OZDAGLAR, Convex Analysis and Optimization, Athena Scientific, Belmont, MA, 2003.
3. J. BIOUCAS-DIAS and M. FIGUEIREDO, A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration, IEEE Trans. Image Process., 16 (2007), pp. 2980-2991.
4. J. CARTER, Dual Methods for Total Variation-Based Image Restoration, Ph.D. thesis, UCLA, Los Angeles, CA, 2002.
5. A. CHAMBOLLE, An algorithm for total variation minimization andapplications, J. Math. Imaging Vision, 20 (2004), pp. 89-97.
6. A. CHAMBOLLE, Total variation minimization and a class of binary MRF models, in Energy Minimization Methods in Computer Vision and Pattern Recognition, Lecture Notes in Comput. Sci. 3757, Springer, Berlin, 2005, pp. 136-152.
7. R. CHAN, T. CHAN, and C. WONG, Cosine transform based preconditioners for total variation deblurring, IEEE Trans. Image Process., 8 (1999), pp. 1472-1478.
8. T. F. CHAN and K. CHEN, An optimization-based multilevel algorithm for total variation image denoising, Multiscale Model. Simul., 5 (2006), pp. 615-645.
9. T. F. CHAN, G. H. GOLUB, and P. MULET, A nonlinear primal-dual method for total variationbased image restoration, SIAM J. Sci. Comput., 20 (1999), pp. 1964-1977.
10. T. F. CHAN and P. MULET, On the convergence of the lagged diffusivity fixed point method in total variation image restoration, SIAM J. Numer. Anal., 36 (1999), pp. 354-367.
11. T. CHAN, M. NG, A. YAU, and A. YIP, Superresolution image reconstruction using fast inpainting algorithms, Appl. Comput. Harmon. Anal., 23 (2007), pp. 3-24.
12. P. L. COMBETTES and V. R. WAJS, Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., 4 (2005), pp. 1168-1200.
13. 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 (2004), pp. 1413-1457.
14. M. FIGUEIREDO and R. NOWAK, An EM algorithm for wavelet-based image restoration, IEEE Trans. Image Process., 12 (2003), pp. 906-916.
15. 1 norms for image restoration, SIAM J. Sci. Comput., 27 (2006), pp. 1881-1902.
16. M. HINTERMUÜlLER, K. ITO, and K. KUNISCH, The primal-dual active set strategy as a semismooth Newton method, SIAM J. Optim., 13 (2003), pp. 865-888.
17. M. HINTERMUÜller and K. KUNISCH, Total bounded variation regularization as a bilaterally constrained optimization problem, SIAM J. Appl. Math., 64 (2004), pp. 1311-1333.
18. M. HINTERMUÜller and G. STADLER, An infeasible primal-dual algorithm for total bounded variation-based inf-convolution-type image restoration, SIAM J. Sci. Comput., 28 (2006), pp. 1-23.
19. D. KRISHNAN, P. LIN, and X. TAI, An efficient operator splitting method for noise removal in images, Commun. Comput. Phys., 1 (2006), pp. 847-858.
20. Y. LI and F. SANTOSA, A computational algorithm for minimizing total variation in image reconstruction, IEEE Trans. Image Process., 5 (1996), pp. 987-995.
21. F.-R. LIN, M. K. NG, and W.-K. CHING, Factorized banded inversepreconditioners for matrices with Toeplitz structure, SIAM J. Sci. Comput., 26 (2005), pp. 1852-1870.
22. M. LYSAKER and X. TAI, Noise removal using smoothed normals andsurface fitting, IEEE Trans. Image Process., 13 (2004), pp.1345-1357.
23. Y. NESTEROV, Smooth minimization of non-smooth functions, Math. Program. Ser. A, 103 (2005) pp. 127-152.
24. M. NG, Iterative Methods for Toeplitz Systems, Oxford University Press, New York, 2004.
25. M. K. NG, R. H. CHAN, and W.-C. TANG, A fast algorithm for deblurring models with Neumann boundary conditions, SIAM J. Sci. Comput., 21 (1999), pp. 851-866.
26. M. NG, L. QI, Y. YANG, and Y. HUANG, On semismooth Newton's methods for total variation minimization, J. Math. Imaging Vision, 27 (2007), pp. 265-276.
27. Z. OPIAL, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), pp. 591-597.
28. L. RUDIN, S. OSHER, and E. FATEMI, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259-268.
29. L. VESE and S. OSHER, Modeling textures with total variation minimization and oscillating patterns in image processing, J. Sci. Comput., 19 (2003), pp. 553-572.
30. C. R. VOGEL and M. E. OMAN, Iterative methods for total variation denoising, SIAM J. Sci. Comput., 17 (1996), pp. 227-238.