A generalized accelerated proximal gradient approach for total-variation-based image restoration

IEEE Transactions on Image Processing

Volumn 20, Issue 10, 2011, Pages 2748-2759

  Zuo, Wangmeng ^a   Lin, Zhouchen ^b  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b MICROSOFT RESEARCH ASIA   (China)

Author keywords

Convex optimization; image restoration; proximal gradient algorithm; regularization; total variation (TV)

Indexed keywords

AUXILIARY VARIABLES; CONVERGENCE RATES; FASTER CONVERGENCE; GRADIENT ALGORITHM; GRADIENT APPROACH; IMAGE DE-NOISING; IMAGE RESTORATION PROBLEM; LIPSCHITZ CONSTANT; NUMBER OF ITERATIONS; PARTIAL DERIVATIVES; POSITIVE-DEFINITE MATRICES; REGULARIZATION; TOTAL VARIATION;

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; CONVEX OPTIMIZATION; EXPERIMENTS; IMAGE RECONSTRUCTION; RESTORATION;

PROBLEM SOLVING;

EID: 80052882112     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2011.2131665     Document Type: Article

References (37)

1. H. Andrews and B. Hunt, Digital Image Restoration. Englewood Cliffs, NJ: Prentice-Hall, 1977.
2. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging. Bristol, U.K.: IOP, 1998.
3. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Phys. D, vol. 60, no. 1-4, pp. 259-268, 1992.
4. D. Donoho and I. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika, vol. 81, no. 3, pp. 425-455, 1994.
5. D. Donoho and I. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," J. Amer. Statist. Assoc., vol. 90, no. 432, pp. 1200-1224, 1995. (Pubitemid 126093135)
6. G. Peyre, S. Bougleux, and L. Cohen, "Non-local regularization of inverse problems," in Proc. Eur. Conf. Comput. Vis., 2008, pp. 57-68.
7. W. Dong, L. Zhang, G. Shi, and X. Wu, "Image deblurring and superresolution by adaptive sparse domain selection and adaptive regularization," IEEE Trans. Image Process., to be published.
8. A. Chambolle, "An algorithm for total variation minimization and applications," J. Math. Imag. Vis., vol. 20, no. 1-2, pp. 89-97, 2004.
9. T. Chan and C.-K. Wong, "Total variation blind deconvolution," IEEE Trans. Image Process., vol. 7, no. 3, pp. 370-375, Mar. 1998. (Pubitemid 128745355)
10. S. Ma,W. Yin, Y. Zhang, and A. Chakraborty, "An efficient algorithm for compressed MR imaging using total variation and wavelets," in Proc. IEEE Conf. Comput. Vis. Pattern Recognit., 2008, pp. 1-8.
11. W. Yin, T. Chen, X. Zhou, and A. Chakraborty, "Background correction for cDNA microarray image using the TV+l1 model," Bioinformatics, vol. 21, no. 10, pp. 2410-2416, 2005. (Pubitemid 40731597)
12. A. Beck and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM J. Imag. Sci., vol. 2, no. 1, pp. 183-202, Mar. 2009.
13. J. Bioucas-Dias, "Bayesian wavelet-based image deconvolution: A GEM algorithm exploiting a class of heavy-tailed priors," IEEE Trans. Image Process., vol. 15, no. 4, pp. 937-951, Apr. 2006.
14. J. Bioucas-Das and M. Figueiredo, "A new twist: Two step iterative shrinkage/thresholding algorithms for image restoration," IEEE Trans. Image Process., vol. 16, no. 12, pp. 2992-3004, Dec. 2007. (Pubitemid 350201232)
15. M. Figueiredo and R. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process., vol. 12, no. 8, pp. 906-916, Aug. 2003.
16. Y. Boykov, O. Veksler, and R. Zabih, "Fast approximate energy minimization via graph cuts," IEEE Trans. Pattern Anal. Mach. Intell., vol. 23, no. 11, pp. 1222-1239, Nov. 2001. (Pubitemid 33137959)
17. D. Goldfarb and W. Yin, "Second-order cone programming methods for total variation-based image restoration," SIAM J. Sci. Comput., vol. 27, no. 2, pp. 622-645, 2005.
18. P. Combettes and V. Wajs, "Signal recovery by proximal forwardbackward splitting," SIAM J. Multiscale Model. Simul., vol. 4, no. 4, pp. 1168-1200, 2005. (Pubitemid 44932287)
19. I. Daubechies, M. Defriese, and C. D. Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math., vol. 57, no. 11, pp. 1413-1457, 2004. (Pubitemid 39427442)
20. K. Bredies and D. Lorenz, "Linear convergence of iterative soft-thresholding," J. Fourier Anal. Appl., vol. 14, no. 5-6, pp. 813-837, Dec. 2008.
21. A. Beck and M. Teboulle, "Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems," IEEE Trans. Image Process., vol. 18, no. 11, pp. 2419-2434, Nov. 2009.
22. A. Ganesh, Z. Lin, J. Wright, L. Wu, M. Chen, and Y. Ma, "Fast algorithms for recovering a corrupted low-rank matrix," in Proc. Int. Workshop Comput. Adv. Multi-Sens. Adaptive Process., 2009, pp. 213-216.
23. P. Tseng, "On accelerated proximal gradient methods for convex-concave optimization," SIAM J. Optim., , to be published.
24. K.-C. Toh and S.Yun, "An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems," Pac. J. Optim., vol. 6, no. 3, pp. 615-640.
25. D. Goldfarb and W. Yin, "Parametric maximum flow algorithms for fast total variation minimization," SIAM J. Sci. Comput., vol. 31, no. 5, pp. 3712-3743, 2009.
26. M. Afonso, J. Bioucas-Dias, and M. Figueiredo, "Fast image recovery using variable splitting and constrained optimization," IEEE Trans. Image Process., vol. 19, no. 9, pp. 2345-2356, Sep. 2010.
27. Y. Wang, J. Yang, W. Yin, and Y. Zhang, "A new alternating minimization algorithm for total variation image reconstruction," SIAM J. Imag. Sci., vol. 1, no. 3, pp. 248-272, Jul. 2008.
28. T. Goldstein and S. Osher, "The split Bregman method for l1 regularized problems," SIAM J. Imag. Sci., vol. 2, no. 2, pp. 323-343, 2009.
29. J. Yang, W. Yin, Y. Zhang, and Y. Wang, "A fast algorithm for edgepreserving variational multichannel image restoration," SIAM J. Imag. Sci., vol. 2, no. 2, pp. 569-592, 2008.
30. S. Wright, R. Nowak, and M. Figueiredo, "Sparse reconstruction by separable approximation," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), Apr. 2008, pp. 3373-3376.
31. 2)," Soviet Math. Doklady, vol. 27, no. 2, pp. 372-376, 1983.
32. G. Golub and C. Loan, Matrix Computation, 3rd ed. Baltimore, MD: The John Hopkins Univ. Press, 1996.
33. M. Figueiredo and J. Bioucas-Dias, "Restoration of Poissonian images using alternating direction optimization," IEEE Trans. Image Process., vol. 19, no. 12, pp. 3133-3145, Dec. 2010.
34. M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, "An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems," IEEE Trans. Image Processing, vol. 20, no. 3, pp. 681-695, Mar. 2011.
35. P. Combettes and J.-C. Pesquet, "A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery," IEEE J. Sel. Topics Signal Process., vol. 1, no. 4, pp. 564-574, Dec. 2007. (Pubitemid 351266623)
36. E. Esser, Applications of Lagrangian-Based Alternating Direction Methods and Connections to Split-Bregman Dept. Comput. Appl. Math., Univ. California, Los Angeles, CA, Tech. Rep. 09-31, Apr. 2009.
37. S. Setzer, "Operator splittings, Bregman methods and frame shrinkage in image processing," Int. J. Comput. Vis., vol. 92, no. 33, pp. 265-280, 2011.