An efficient primal-dual method for L1TV image restoration

SIAM Journal on Imaging Sciences

Volumn 2, Issue 4, 2009, Pages 1168-1189

  Dong, Yiqiu ^a   Hintermüller, Michael ^b   Neri, Marrick ^c  

^a UNIVERSITY OF GRAZ   (Austria)

^b HUMBOLDT UNIVERSITY   (Germany)

^c UNIVERSITY OF THE PHILIPPINES   (Philippines)

Author keywords

Deblurring; Duality; Random valued impulse noise; Salt and pepper noise; Semismooth newton; Total variation regularization; 1 data fitting

Indexed keywords

IMAGE DENOISING; IMAGE RECONSTRUCTION; IMPULSE NOISE;

DATA FITTINGS; DEBLURRING; DUALITY; RANDOM-VALUED IMPULSE NOISE; SALT-AND-PEPPER NOISE; SEMISMOOTH; TOTAL VARIATION REGULARIZATION;

RESTORATION;

EID: 77953704692     PISSN: None     EISSN: 19364954     Source Type: Journal    
DOI: 10.1137/090758490     Document Type: Article

References (25)

1. L. Bar, N. Sochen, and N. Kiryati, Deblurring of color images corrupted by salt-and-pepper noise, IEEE Trans. Image Process., 16 (2007), pp. 1101-1111.
2. L. Bar, N. Sochen, and N. Kiryati, Image deblurring in the presence of impulsive noise, Int. J. Comput. Vision, 70 (2006), pp. 279-298.
3. L. Bar, N. Sochen, and N. Kiryati, Image deblurring in the presence of salt-and-pepper noise, in Proceedings of 5th International Conference on Scale Space and PDE Methods in Computer Vision, Lecture Notes in Comput. Sci. 3459, Springer, Berlin, 2005, pp. 107-118.
4. A. Chambolle, An algorithm for total variation minimization and application, J. Math. Imaging Vision, 20 (2004), pp. 89-97.
5. 1function approximation, SIAM J. Appl. Math., 65 (2005), pp. 1817-1837.
6. T. F. Chan, G. H. Golub, and P. Mulet, A nonlinear primal-dual method for total variation-based image restoration, SIAM J. Sci. Comput., 20 (1999), pp. 1964-1977.
7. I. Ekeland and R. Témam, Convex Analysis and Variational Problems, Classics Appl. Math. 28, SIAM, Philadelphia, 1999.
8. H. Fu, M. K. Ng, M. Nikolova, and J. L. Barlow, Efficient minimization methods of mixed ℓ2-ℓ1 and ℓ1-ℓ1 norms for image restoration, SIAM J. Sci. Comput., 27 (2006), pp. 1881-1902.
9. G. Gilboa, N. Sochen, and Y. Zeevi, Texture preserving variational denoising using an adaptive fidelity term, in Proceedings of the IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, Nice, France, 2003, pp. 137-144.
10. E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Monogr. Math. 80, Birkhäuser-Verlag, Basel, 1984.
11. M. Hintermüller, K. Ito, and K. Kunisch, The primal-dual active set strategy as a semismooth Newton method, SIAM J. Optim., 13 (2002), pp. 865-888.
12. M. Hintermüller and K. Kunisch, Total bounded variation regularization as bilaterally constrained optimization problem, SIAM J. Appl. Math., 64 (2004), pp. 1311-1333.
13. M. Hintermüller 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.
14. P. J. Huber, Robust regression: Asymptotics, conjectures, and Monte Carlo, Ann. Statist., 1 (1973), pp. 799-821.
15. D. Mumford and J. Shah, Optimal approximation by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math., 17 (1989), pp. 577-685.
16. M. Nikolova, Minimizers of cost-functions involving nonsmooth data-fidelity terms. Application to the processing of outliers, SIAM J. Numer. Anal., 40 (2002), pp. 965-994.
17. M. Nikolova, A variational approach to remove outliers and impulse noise, J. Math. Imaging Vision, 20 (2004), pp. 99-120.
18. L. Q. Qi and J. Sun, A nonsmooth version of Newton’s method, Math. Programming, 58 (1993), pp. 353-367.
19. L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259-268.
20. Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., SIAM, Philadelphia, 2003.
21. D. Strong and T. Chan, Edge-preserving and scale-dependent properties of total variation regularization, Inverse Problems, 19 (2003), pp. 165-187.
22. A. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems, Winston and Sons, Washington, D.C., 1977.
23. C. R. Vogel, Computational Methods for Inverse Problems, Frontiers Appl. Math. 23, SIAM, Philadelphia, 2002.
24. J. Yang, Y. Zhang, and W. Yin, An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise, SIAM J. Sci. Comput., 31 (2009), pp. 2842-2865.
25. 1 model for multiscale decomposition, Multiscale Model. Simul., 6 (2007), pp. 190-211.