Framelet algorithms for De-blurring images corrupted by impulse plus Gaussian noise

IEEE Transactions on Image Processing

Volumn 20, Issue 7, 2011, Pages 1822-1837

  Li, Yan Ran ^a   Shen, Lixin ^b   Dai, Dao Qing ^c   Suter, Bruce W ^d  

^a SHENZHEN UNIVERSITY   (China)

^b SYRACUSE UNIVERSITY   (United States)

^c SUN YAT SEN UNIVERSITY   (China)

^d AIR FORCE RESEARCH LABORATORY   (United States)

Author keywords

Adaptive iterated algorithm; parameter free; tight framelet

Indexed keywords

ADAPTIVE ITERATED ALGORITHM; DEBLURRING; DEBLURRING ALGORITHMS; FIDELITY TERM; FRAMELET; GAUSSIAN AND IMPULSE NOISE; GEOMETRIC FEATURE; IMAGE DEBLURRING; MUMFORD-SHAH; PARAMETER-FREE; REGULARIZER; TIGHT FRAMELET; VISUAL QUALITIES;

GAUSSIAN DISTRIBUTION; GAUSSIAN NOISE (ELECTRONIC); IMAGE RECONSTRUCTION; IMPULSE NOISE;

ADAPTIVE ALGORITHMS;

EID: 79959596131     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2010.2103950     Document Type: Article

References (61)

1. A. Tikhonov and V. Arsenin, Solutions to Ill-Posed Problems. New York: Wiley, 1977.
2. D. Geman and G. Reynolds, "Constrained restoration and the recovery of discontinuities," IEEE Trans. Pattern Anal. Mach. Intell., vol. 14, no. 3, pp. 367-383, Mar. 1992.
3. L. Rudin and S. Osher, "Total variation based image restoration with free local constraints," in IEEE Int. Conf. Image Process., 1994, pp. 31-35.
4. G. Aubert and L.Vese, "A variational method in image recovery," SIAM J. Numer. Anal., vol. 34, no. 5, pp. 1948-1979, 1997. (Pubitemid 127463579)
5. C. Vogel and M. Oman, "Fast, robust total variation-based reconstruction of noisy, blurred images," IEEE Trans. Image Process., vol. 7, no. 6, pp. 813-824, Jun. 1998. (Pubitemid 128745393)
6. A. Chambolle, "An algorithm for total variation minimization and applications," J. Math. Imaging Vis., vol. 20, pp. 89-97, 2004.
7. P. Combettes and J. Pesquet, "Image restoration subject to a total variation constraint," IEEE Trans. Image Process., vol. 13, no. 9, pp. 1213-1222, Sep. 2004.
8. T. Goldstein and S. Osher, "The split Bregman method for l1 regularization problems," SIAM J. Imaging Sci., vol. 2, pp. 323-343, 2009.
9. S. Osher,M. Burger, D. Goldfarb, J. Xu, and W. Yin, "An iterative regularization method for total variation-based image restoration," Multiscale Model Simul., vol. 4, no. 2, pp. 460-489, 2005. (Pubitemid 43885248)
10. R. Coifman and D. Donoho, "Translation-invariant de-noising," in Wavelet and Statistics, Springer Lecture Notes in Statistics. New York: Springer-Verlag, 1990, vol. 103, pp. 125-150.
11. M. Crouse, R. D. Nowak, and R. Baraniuk, "Wavelet-based statistical signal processing using hidden Markov models," IEEE Trans. Signal Process., vol. 46, no. 4, pp. 886-902, Apr. 1998. (Pubitemid 128743828)
12. M. Figueiredo and R. D. Nowak, "Wavelet-based image estimation: An empirical Bayes approach using Jeffreys' noninformative prior," IEEE Trans. Image Process., vol. 10, no. 9, pp. 1322-1331, 2001. (Pubitemid 32949956)
13. J. Portilla, V. Strela, M. Wainwright, and E. P. Simoncelli, "Image denoising using scale mixtures of Gaussians in thewavelet domain," IEEE Trans. Image Process., vol. 12, no. 11, pp. 1338-1351, Nov. 2003.
14. L. Shen, M. Papadakis, I. A. Kakadiaris, I. Konstantinidis, D. Kouri, and D. Hoffman, "Image denoising using a tight frame," IEEE Trans. Image Process., vol. 15, no. 5, pp. 1254-1263, May 2006.
15. M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester, "Image inpainting," in Proc. SIGGRAPH, New Orleans, LA, 2000, pp. 417-424. (Pubitemid 32394006)
16. Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, ser. University Lecture Series. Providence, RI: AMS, 2001, vol. 22.
17. M. Bertalmio, L. Vese, G. Sapiro, and S. Osher, "Simultaneous structure and texture image inpainting," IEEE Trans. Image Process., vol. 12, no. 8, pp. 882-889, Aug. 2003.
18. J. Starck, M. Elad, and D. Donoho, "Image decomposition via the combination of sparse representations and a variational approach," IEEE Trans. Image Process., vol. 114, no. 10, pp. 1570-1582, Oct. 2005. (Pubitemid 41623087)
19. Y. Kim and L. Vese, "Image recovery using functions of bounded variation and sobolev spaces of negative differentiability," Inverse Problem Imaging, vol. 3, no. 1, pp. 43-68, 2009.
20. T. Chan, J. Shen, and H. M. Zhou, "Total variation wavelet inpainting," J. Math. Imaging Vis., vol. 25, no. 1, pp. 107-125, Jul. 2006. (Pubitemid 44544743)
21. J. F. Cai, R. Chan, L. Shen, and Z. Shen, "Fast two-phase image deblurring under impulse noise," Numer. Math., vol. 112, pp. 509-533, 2009.
22. A. Bovik, Handbook of Image and Video Processing. San Diego, CA: Academic, 2000.
23. H. Hwang and R. Haddad, "Adaptive median filters: New algorithms and results," IEEE Trans. Image Process., vol. 4, no. 4, pp. 499-502, Apr. 1995.
24. G. Pok, J. C. Liu, and A. S. Nair, "Selective removal of impulse noise based on homogeneity level information," IEEE Trans. Image Process., vol. 12, no. 1, pp. 85-92, Jan. 2003.
25. J. F. Cai, R. Chan, and Z. Shen, "A framelet-based image inpainting algorithm," Appl. Comput. Harmon. Anal., vol. 24, pp. 131-149, Mar. 2008. (Pubitemid 351215929)
26. J. F. Cai, R. Chan, L. Shen, and Z. Shen, "Convergence analysis of tight framelet approach for missing data recovery," Adv. Comput. Math., vol. 31, pp. 87-133, 2009.
27. M. Nikolova, "A variational approach to remove outliers and impulse noise," J. Math. Imaging Vis., vol. 20, no. 1/2, pp. 99-120, Jan. 2004.
28. R. Chan, S. D. Riemenschneider, L. Shen, and Z. Shen, "Tight frame: An efficient way for high-resolution image reconstruction," Appl. Comput. Harmon. Anal., vol. 17, no. 1, pp. 91-115, Jul. 2004.
29. L. Bar, A. Brook, 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. (Pubitemid 46542396)
30. L. Bar, N. Sochen, and N. Kiryati, "Image deblurring in the presence of impulsive noise," Int. J. Comput. Vis., vol. 70, no. 3, pp. 279-298, Dec. 2006. (Pubitemid 44127250)
31. J. F. Cai, R. Chan, and M. Nikolova, "Two-phase methods for deblurring images corrupted by impulse plus Gaussian noise," Inverse Problem Imaging, vol. 2, pp. 187-204, May 2008.
32. J. F. Cai, R. Chan, and M. Nikolova, "Fast two-phase image deblurring under impulse noise," J. Math. Imaging Vis., vol. 36, pp. 46-53, 2010.
33. D. Mumford and J. Shah, "Optimal approximation by piecewise smooth functions and associated variational problems," Comm. Pure Appl. Math., vol. 42, pp. 577-685, 1989.
34. L. Amborsio and V. M. Tortorelli, "Approximation of functionals depending on jumps by elliptic functionals via convergence," Comm. Pure Appl. Math., vol. XLIII, pp. 999-1036, 1990.
35. R. Gonzalez and R. Woods, Digital Image Processing. Boston, MA: Addison-Wesley, 1993.
36. S.Ko and Y. Lee, "Adaptive center weighted median filter," IEEE Trans. Circuits Syst. II, Fundam. Appl. Theory, vol. 38, no. , pp. 984-993, 1998.
37. R. Chan, C. W. 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. 12, pp. 1479-1485, Dec. 2005. (Pubitemid 41623079)
38. A. Ron and Z. Shen, "Affine system in l2(rd): The analysis of the analysis operator," J. Funct. Anal., vol. 148, pp. 408-447, 1997. (Pubitemid 127171400)
39. Y. R. Li, D. Q. Dai, and L. Shen, "Multiframe super-resolution reconstruction using sparse directional regularization," IEEE Trans. Circuits Syst. Video Technol., vol. 20, no. 7, pp. 945-956, Jul. 2010.
40. R. Chan, S. D. Riemenschneider, L. Shen, and Z. Shen, "Tight frame: An efficient way for high-resolution image reconstruction," Appl. Comput. Harmon. Anal., vol. 17, no. 1, pp. 91-115, Jul. 2004.
41. D. Donoho and I. Johnstone, "Ideal spatial adaptation by wavelet shrinkage," Biometrica, vol. 81, no. 3, pp. 425-455, Aug. 1994.
42. S. Didas and J.Weickert, "Integrodifferential equations for continuous multiscale wavelet shrinkage," IPI, vol. 1, no. 1, pp. 47-62, 2007.
43. S. Didas, G. Steidl, and J. Weickert, P. Schelkens, T. Ebrahimi, G. Christobal, and F. Truchetet, Eds., "Discrete multiscale wavelet shrinkage and integrodifferential equations," in Proc. SPIE-Opt. Digital Image Processing-Photonics Europe, 2008, vol. 7000.
44. P. Huber, Robust Statistics, 2nd ed. Hoboken, NJ: Wiley, 2009.
45. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D, vol. 60, pp. 259-268, 1992.
46. T. Chan, S. Esedoglu, and F. Park, "Image decomposition combining staircase reduction and texture extraction," J. Vis. Comm. Image Rep., vol. 18, no. 6, pp. 464-486, 2007. (Pubitemid 47633232)
47. P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, "Deterministic edgepreserving regularization in computed imaging," IEEE Trans. Image Process., vol. 6, no. 12, pp. 298-311, Dec. 1997. (Pubitemid 127766386)
48. J. M. Bioucas Dias and M. A. T. 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)
49. R. Chan, S. D. Riemenschneider, L. Shen, and Z. Shen, "High-resolution image reconstruction with displacement errors: A framelet approach," Int. J. Imaging Syst. Technol., vol. 14, no. 3, pp. 91-104, 2004.
50. I. Daubechies, M. Defrise, and C. D. Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Comm. Pure Appl. Math., vol. 57, pp. 1413-1541, 2004.
51. M. Figueiredo and R. D. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process., vol. 12, no. 8, pp. 906-916, Aug. 2003.
52. M. Kang and A. Katsaggelos, "General choice of the regularization functional in regularized image-restoration," IEEE Trans. Image Process., vol. 4, no. 5, pp. 594-602, May 1995.
53. L. Sendur and I. W. Selesnick, "Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency," IEEE Trans. Signal Process., vol. 50, no. 11, pp. 2744-2756, Nov. 2002. (Pubitemid 35312118)
54. A. Hyvarinen, "Sparse code shrinkage: Denoising of non-gaussian data by maximum likelihood estimation," Neural Comput., vol. 11, pp. 1739-1768, 1999.
55. Y. Nesterov, "Smooth minimization of non-smooth functions," Math. Programming, vol. 103, pp. 127-152, 2005. (Pubitemid 40537674)
56. A. Beck and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM J. Imaging Sci., vol. 2, no. 1, pp. 183-202, 2009.
57. E. Esser, X. Zhang, and T. Chan, "A genetral framework for a class of first order primal-dual algorithms for TV minimization," Center for Appl. Math., UCLA, 2009.
58. S. Becker, J. Bobin, and E. Candes, "NESTA: A fast and accurate firstorder method for sparse recovery," Stanford Univ., 2009.
59. M. Fadili and G. Peyre, "Total variation projection with first order schemes," IEEE Trans. Image Process., vol. 20, no. 3, pp. 657-669, Mar. 2011.
60. P. L. Combettes and J. C. Pesquet, , H. H. Bauschke, R. Burachik, P. L. Combettes, V. Elser, D. R. Luke, and H. Wolkowicz, Eds., "Proximal splitting methods in signal processing," in Fixed-Point Algorithms For Inverse Problems in Science and Engineering. New York: Springer- Verlag, 2010.
61. Y. Dong, R. Chan, and S. Xu, "A detection statistic for random-valued impulse noise," IEEE Trans. Signal Process., vol. 16, no. 4, pp. 1112-1120, 2007. (Pubitemid 46542397)