Adaptive variational method for restoring color images with high density impulse noise

International Journal of Computer Vision

Volumn 90, Issue 2, 2010, Pages 131-149

  Liu, Jun ^a   Huang, Haiyang ^a   Huan, Zhongdan ^a   Zhang, Haili ^b  

^a BEIJING NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF FLORIDA   (United States)

Author keywords

Color image; Deblurring and denoising; EM algorithm; Impulse noise; Split Bregman method; Variational regularization methods

Indexed keywords

COLOR IMAGES; DEBLURRING AND DENOISING; EM ALGORITHM; SPLIT BREGMAN METHOD; VARIATIONAL REGULARIZATION;

COLOR; CONTROL SYSTEM ANALYSIS; DYNAMIC LOADS; IMPULSE NOISE; NOISE POLLUTION CONTROL; NUMERICAL METHODS; PROBABILITY; PROBABILITY DENSITY FUNCTION; RESTORATION;

ALGORITHMS;

EID: 79957529391     PISSN: 09205691     EISSN: 15731405     Source Type: Journal    
DOI: 10.1007/s11263-010-0351-9     Document Type: Article

References (40)

1. L. Bar A. Brook N. Sochen N. Kiryati 2007 Deblurring of color images corrupted by impulsive noise IEEE Transactions on Image Processing 16 4 1101 1111 10.1109/TIP.2007.891805 2463912 (Pubitemid 46542396)
2. L. Bar N. Sochen N. Kiryati 2006 Image deblurring in the presence of impulsive noise International Journal of Computer Vision 70 279 298 10.1007/s11263-006-6468-1 (Pubitemid 44127250)
3. Bilmes, J. (1998). A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.613.
4. P. Blomgren T. F. Chan 1998 Color TV: total variation methods for restoration of vector-valued images IEEE Transactions on Image Processing 7 3 304 309 10.1109/83.661180
5. X. Bresson T. F. Chan 2008 Fast dual minimization of the vectorial total variation norm and applications to color image processing Inverse Problems and Imaging 2 4 455 484 1188.68337 10.3934/ipi.2008.2.455 2558277
6. X. Bresson S. Esedoglu P. Vandergheynst J. Thiran S. Osher 2007 Fast global minimization of the active contour/snake model Journal of Mathematical Imaging and Vision 28 151 167 10.1007/s10851-007-0002-0 2362922 (Pubitemid 47312505)
7. J. Cai R. Chan M. Nikolova 2008 Two-phase approach for deblurring images corrupted by impulse plus Gaussian noise Inverse Problems and Imaging 2 187 204 1154.94306 2395140
8. J. Cai R. Chan M. Nikolova 2009 Fast two-phase image deblurring under impulse noise Journal of Mathematical Imaging and Vision 10.1007/s10851-009- 0169-7
9. A. Chambolle 2004 An algorithm for total variation minimization and applications Journal of Mathematical Imaging and Vision 20 89 97 10.1023/B:JMIV.0000011320.81911.38 2049783
10. T. Chan G. Golub P. Mulet 1999 A nonlinear primal-dual method for total variation-based image restoration SIAM Journal on Scientific Computing 20 1964 1977 0929.68118 10.1137/S1064827596299767 1694649
11. R. Chan C. Ho M. Nikolova 2005 Salt-and-pepper noise removal by median-type noise detectors and edge-preserving regularization IEEE Transactions on Image Processing 14 10 1479 1485 10.1109/TIP.2005.852196 (Pubitemid 41623079)
12. Chan, T., & Shen, J. (2005). Image processing and analysis-variational, PDE, wavelet, and stochastic methods (pp. 207-243). Philadelphia: SIAM.
13. T. Chen H. Wu 2001 Space variant median filters for the restoration of impulse noise currupted images IEEE Transactions on Circuits and Systems Part II: Analog and Digital Signal Processing 48 784 789 1012.94505 10.1109/82.959870
14. J. Darbon M. Sigelle 2005 A fast and exact algorithm for total variation minimization Pattern Recognition and Image Analysis 3522 351 359
15. J. Douglas H. H. Rachford 1956 On the numerical solution of heat conduction problems in two and three space variables Transactions of the American Mathematical Society 82 2 421 439 0070.35401 84194
16. H. Eng K. Ma 2001 Noise adaptive soft-switching median filter IEEE Transactions on Image Processing 10 242 251 1039.68783 10.1109/83.902289 (Pubitemid 32254594)
17. Esser, E. (2009). Applications of Lagrangian-based alternating direction methods and connections to split Bregman. UCLA CAM Report 09-31.
18. G. Gilboa S. Osher 2007 Nonlocal linear image regularization and supervised segmentation Multiscale Modeling and Simulation 6 595 630 1140.68517 10.1137/060669358 2338496
19. G. Gilboa S. Osher 2008 Nonlocal operators with applications to image processing Multiscale Modeling and Simulation 7 1005 1028 1181.35006 10.1137/070698592 2480109
20. Goldstein, T., & Osher, S. (2008). The split Bregman method for L1 regularized problems. UCLA CAM Report 08-29.
21. Y. Huang M. Ng Y. Wen 2009 Fast image restoration methods for impulse and gaussian noises removal IEEE Signal Processing Letters 16 457 460 10.1109/LSP.2009.2016835
22. A. Jalobeanu L. Blanc-Feraud J. Zerubia 2005 An adaptive Gaussian model for satellite image deblurring IEEE Transactions on Image Processing 14 10 1469 1478 10.1109/TIP.2005.851705 (Pubitemid 41623078)
23. R. Lagendijk A. Tekalp J. Biemond 1990 Maximum likelihood image and blur identification: a unifying approach Optical Engineering 29 5 422 435 10.1117/12.55611
24. J. Liu Z. Huan H. Huang H. Zhang 2009 An adaptive method for recovering image from mixed noisy data International Journal of Computer Vision 85 2 182 191 10.1007/s11263-009-0254-9
25. McLachlan, G. J., & Krishnan, T. (2007). The EM algorithm and extensions. New York: John Wiley & Sons Inc.
26. K. Michael H. Chan W. Tang 1999 A fast algorithm for deblurring models with Neumann boundary conditions SIAM Journal on Scientific Computing 21 3 851 866 0951.65038 10.1137/S1064827598341384 1718798
27. D. Mumford J. Shah 1989 Optimal approximations by piecewise smooth functions and associated variational problems Communications on Pure and Applied Mathematics 42 577 685 0691.49036 10.1002/cpa.3160420503 997568
28. M. Nikolova 2004 A variational approach to remove outliers and impulse noise Journal of Mathematical Imaging and Vision 20 99 120 10.1023/B:JMIV. 0000011920.58935.9c 2049784
29. R. Redner H. Walker 1984 Mixture densities, maximum likelihood and the EM algorithm SIAM Review 26 2 195 239 0536.62021 10.1137/1026034 738930
30. Rudin, L., & Osher, S. (1994). Total variation based image restoration with free local constraints. In IEEE ICIP 1994 (Vol. 1, pp. 31-35).
31. L. Rudin S. Osher E. Fatemi 1992 Nonlinear total variation based noise removal algorithms Physica D 60 259 268 0780.49028 10.1016/0167-2789(92)90242-F
32. S. Setzer 2009 Split Bregman algorithm, Douglas-Rachford splitting and frame shrinkage Scale Space and Variational Methods in Computer Vision 5567 464 476 10.1007/978-3-642-02256-2-39
33. Q. Shan J. Jia A. Agarwala 2008 High-quality motion deblurring from a single image ACM Transactions on Graphics (SIGGRAPH) 27 1 10
34. Tai, X., & Wu, C. (2009). Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model. UCLA CAM Report 09-05.
35. Tschumperle, D. (2002). PDEs based regularization of multivalued images and applications. Ph.D. dissertation, Univ. Nice-Sophia Antipolis, Sophia Antipolis, France.
36. Vogel, C. (2002). Computational methods for inverse problems (pp. 53-54). Philadelphia: SIAM.
37. C. Vogel M. Oman 1996 Iterative methods for total variation denoising SIAM Journal on Scientific Computing 17 1 227 238 0847.65083 10.1137/0917016 1375276
38. C. Vogel M. Oman 1998 Fast, robust total variation-based reconstruction of noisy, blurred images IEEE Transactions on Image Processing 7 6 813 824 0993.94519 10.1109/83.679423 1667392
39. J. Yang Y. Zhang W. Yin 2009 An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise SIAM Journal on Scientific Computing 31 4 2842 2865 05770813 10.1137/080732894 2520302
40. W. Zhao A. Pope 2007 Image restoration under significant additive noise IEEE Signal Processing Letters 14 6 401 404 10.1109/LSP.2006.887843 (Pubitemid 46845710)