An efficient two-phase L1-TV method for restoring blurred images with impulse noise

IEEE Transactions on Image Processing

Volumn 19, Issue 7, 2010, Pages 1731-1739

  Chan, Raymond H ^a   Dong, Yiqiu ^b   Hintermuller, Michael ^a,c  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF GRAZ   (Austria)

^c HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Fenchel duality; Image deblurring; Impulse noise; L1 data fitting; Noise detector; Semismooth Newton method; Total variation regularization

Indexed keywords

DATA FITTINGS; FENCHEL DUALITY; IMAGE DEBLURRING; L1 DATA FITTING; SEMISMOOTH NEWTON METHOD; TOTAL VARIATION REGULARIZATION;

COMPUTATIONAL EFFICIENCY; DATA HANDLING; DETECTORS; IMAGE RECONSTRUCTION; NEWTON-RAPHSON METHOD; NUMERICAL ANALYSIS; PIXELS; RESTORATION; VARIATIONAL TECHNIQUES;

IMPULSE NOISE;

EID: 77953709191     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2010.2045148     Document Type: Article

References (28)

1. A. Bovik, Handbook of Image and Video Processing. New York: Academic, 2000.
2. H. Hwang and R. Haddad, "Adaptive median filters: New algorithms and results," IEEE Trans. Image Process., vol.4, pp. 499-502, Apr. 1995.
3. S. Zhang and M. Karim, "A new impulse detector for switching median filters," IEEE Signal Process. Lett., vol.9, no.11, pp. 360-363, Nov. 2002.
4. I. Aizenberg, C. Butakoff, and D. Paliy, "Impulsive noise removal using threshold Boolean filtering based on the impulse detecting functions," IEEE Signal Process. Lett., vol.12, no.1, pp. 63-66, Jan. 2005.
5. M. Nikolova, "A variational approach to remove outliers and impulse noise," J. Math. Imag. Vis., vol.20, pp. 99-120, 2004.
6. R. Chan, C. Ho, and M. Nikolova, "Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization," IEEE Trans. Image Process., vol.14, no.10, pp. 1479-1485, Oct. 2005.
7. R. H. Chan, C.-W. Ho, C.-Y. Leung, and M. Nikolova, "Minimization of detail-preserving regularization functional by Newton's method with continuation," in Proc. Int. Conf. Image Processing, 2005, pp. 125-128.
8. T. Chen and H.Wu, "Adaptive impulse detection using center-weighted median filters," IEEE Signal Process. Lett., vol.8, no.1, pp. 1-3, Jan. 2001.
9. R. Chan, C. Hu, and M. Nikolova, "An iterative procedure for removing random-valued impulse noise," IEEE Signal Process. Lett., vol.11, no.12, pp. 921-924, Dec. 2004.
10. R. Garnett, T. Huegerich, C. Chui, and W.-J. He, "A universal noise removal algorithm with an impulse detector," IEEE Trans. Image Process., vol.14, no.11, pp. 1747-1754, Nov. 2005.
11. Y. Dong and S. Xu, "A new directional weighted median filter for removal of random-valued impulse noise," IEEE Signal Process. Lett., vol.14, no.3, pp. 193-196, Mar. 2007.
12. Y. Dong, R. H. Chan, and S. Xu, "A detection statistic for randomvalued impulse noise," IEEE Trans. Image Process., vol.16, no.4, pp. 1112-1120, Apr. 2007.
13. A. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems. Washington DC: Winston and Sons, 1977.
14. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D, vol.60, pp. 259-268, 1992.
15. J. Bect, L. Blanc-Féraud, G. Aubert, and A. Chambolle, "A unified variational framework for image restoration," in Proc. ECCV, 2004, vol. LNCS, no. 3024, pp. 1-13.
16. L. Bar, N. Sochen, and N. Kiryati, "Image deblurring in the presence of salt-and-pepper noise," in Proc. 5th Int. Conf. Scale Space and PDE Methods in Computer Vision, 2005, vol. LNCS, no. 3439, pp. 107-118.
17. L. Bar, N. Sochen, and N. Kiryati, "Image deblurring in the presence of impulsive noise," Int. J. Comput. Vis., vol.70, pp. 279-298, 2006.
18. L. Bar, N. Sochen, and N. Kiryati, "Deblurring of color images corrupted by salt-and-pepper noise," IEEE Trans. Image Process., vol.16, no.4, pp. 1101-1111, Apr. 2007.
19. J. Yang, Y. Zhang, and W. Yin, An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise Submitted [Online]. Available: http://www.caam.rice.edu/∼wy1/paperfiles/ Rice-CAAM-TR08-12.PDF
20. Y. Dong, M. Hintermüller, and M. Neri, "A primal-dual method for TV image denoising," SIAM J. Imag. Sci., vol.2, no.4, pp. 1168-1189, 2009.
21. J. Cai, R. Chan, and M. Nikolova, "Two-phase approach for deblurring images corrupted by impulse plus gaussian noise," Inverse Problems Imag., vol.2, pp. 187-204, 2008.
22. I. Ekeland and R. Témam, Convex Analysis and Variational Problems. Philadelphia, PA: SIAM, 1999, vol.28, Classics Appl. Math.
23. M. Hintermüller and G. Stadler, "An infeasible primal-dual algorithm for total bounded variation-based inf-convolution-type image restoration," SIAM J. Sci. Comput., vol.28, no.1, pp. 1-23, 2006.
24. M. Hintermüller, K. Ito, and K. Kunisch, "The primal-dual active set strategy as a semismooth newton method," SIAM J. Optim., vol.13, pp. 865-888, 2002.
25. M. Hintermüller and K. Kunisch, "Total bounded variation regularization as bilaterally constrained optimization problem," SIAM J. Appl. Math., vol.64, pp. 1311-1333, 2004.
26. F. M. Clarke, Optimization and Nonsmooth Analysis. Hoboken, NJ: Wiley, 1983.
27. P. J. Huber, "Robust regression: Asymptotics, conjectures, and monte carlo," Ann. Statist., vol.1, pp. 799-821, 1973.
28. USC-SIPI Image Database [Online]. Available: http://sipi.usc.edu/ services/ database/Database.html, Univ. Southern California