Group-based sparse representation for image restoration

IEEE Transactions on Image Processing

Volumn 23, Issue 8, 2014, Pages 3336-3351

  Zhang, Jian ^a   Zhao, Debin ^a   Gao, Wen ^b  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b PEKING UNIVERSITY   (China)

Author keywords

compressive sensing; deblurring; Image restoration; inpainting; nonlocal self similarity; sparse representation

Indexed keywords

IMAGE RECONSTRUCTION; OPTIMIZATION;

COMPRESSIVE SENSING; DEBLURRING; INPAINTING; SELF-SIMILARITIES; SPARSE REPRESENTATION;

IMAGE ENHANCEMENT;

ALGORITHM; ARTIFACT; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; PROCEDURES; REPRODUCIBILITY; SAMPLE SIZE; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING; STATISTICAL MODEL;

ALGORITHMS; ARTIFACTS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MODELS, STATISTICAL; REPRODUCIBILITY OF RESULTS; SAMPLE SIZE; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 84904285443     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2014.2323127     Document Type: Article

References (51)

1. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Phys. D, Nonlinear Phenomena, vol. 60, nos. 1-4, pp. 259-268, Nov. 1992.
2. M. R. Banham and A. K. Katsaggelos, "Digital image restoration," IEEE Signal Process. Mag., vol. 14, no. 2, pp. 24-41, Mar. 1997. (Pubitemid 127571670)
3. L. Zhang, W. Dong, D. Zhang, and G. Shi, "Two-stage image denoising by principal component analysis with local pixel grouping," Pattern Recognit., vol. 43, no. 4, pp. 1531-5549, Apr. 2010.
4. A. Chambolle, "An algorithm for total variation minimization and applications," J. Math. Imag. Vis., vol. 20, nos. 1-2, pp. 89-97, Jan./Mar. 2004.
5. W. Dong, G. Shi, and X. Li, "Nonlocal image restoration with bilateral variance estimation: A low-rank approach," IEEE Trans. Image Process., vol. 22, no. 2, pp. 700-711, Feb. 2013.
6. H. Takeda, S. Farsiu, and P. Milanfar, "Kernel regression for image processing and reconstruction," IEEE Trans. Image Process., vol. 16, no. 2, pp. 349-366, Feb. 2007. (Pubitemid 46421678)
7. S. Roth and M. J. Black, "Fields of experts," Int. J. Comput. Vis., vol. 82, no. 2, pp. 205-229, 2009.
8. A. Buades, B. Coll, and J. M. Morel, "A non-local algorithm for image denoising," in Proc. Int. Conf. CVPR, Jun. 2005, pp. 60-65.
9. J. Bioucas-Dias, M. Figueiredo, and J. Oliveira, "Total-variation image decon-volution: A majorization-minimization approach," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., Toulouse, France, May 2006, p. 2.
10. X. Li, "Image recovery from hybrid sparse representation: A deterministic annealing approach," IEEE J. Sel. Topics Signal Process., vol. 5, no. 5, pp. 953-962, Sep. 2011.
11. 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., vol. 20, no. 7, pp. 1838-1857, Jul. 2011.
12. J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman, "Non-local sparse models for image restoration," in Proc. IEEE 12th Int. Conf. Comput. Vis., Tokyo, Japan, Sep. 2009, pp. 2272-2279.
13. J.-F. Cai, H. Ji, C. Liu, and Z. Shen, "Framelet-based blind motion deblurring from a single image," IEEE Trans. Image Process., vol. 21, no. 2, pp. 562-572, Feb. 2012.
14. A. Danielyan, V. Katkovnik, and K. Egiazarian, "BM3D frames and variational image deblurring," IEEE Trans. Image Process., vol. 21, no. 4, pp. 1715-1728, Apr. 2012.
15. W. Dong, L. Zhang, G. Shi, and X. Li, "Nonlocally centralized sparse representation for image restoration," IEEE Trans. Image Process., vol. 22, no. 4, pp. 1620-1630, Apr. 2013.
16. J. Bioucas-Dias 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)
17. 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.
18. 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.
19. M. Duarte, M. Davenport, D. Takhar, J. Laska, and T. Sun, "Singlepixel imaging via compressive sampling," IEEE Signal Process. Mag., vol. 25, no. 2, pp. 83-91, Mar. 2008.
20. J. Zhang, D. Zhao, C. Zhao, R. Xiong, S. Ma, and W. Gao, "Compressed sensing recovery via collaborative sparsity," in Proc. IEEE DCC, Snowbird, UT, USA, Apr. 2012, pp. 287-296.
21. 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.
22. D. Mumford and J. Shah, "Optimal approximations by piecewise smooth functions and associated variational problems," Commun. Pure Appl. Math., vol. 42, no. 5, pp. 577-685, Jul. 1989.
23. A. M. Bruckstein, D. L. Donoho, and M. Elad, "From sparse solutions of systems of equations to sparse modeling of signals and images," SIAM Rev., vol. 51, no. 1, pp. 34-81, 2009.
24. M. Aharon, M. Elad, and A. Bruckstein, "K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation," IEEE Trans. Signal Process., vol. 54, no. 11, pp. 4311-4322, Nov. 2006. (Pubitemid 44637761)
25. M. Elad and M. Aharon, "Image denoising via sparse and redundant representations over learned dictionaries," IEEE Trans. Image Process., vol. 15, no. 12, pp. 3736-3745, Dec. 2006. (Pubitemid 44811686)
26. J. Yang, J. Wright, T. Huang, and Y. Ma, "Image super-resolution via sparse representation," IEEE Trans. Image Process., vol. 19, no. 11, pp. 2861-2873, Nov. 2010.
27. K. Engan, S. O. Aase, and J. H. Hakon-Husoy, "Method of optimal directions for frame design," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., vol. 5. Mar. 1999, pp. 2443-2446.
28. J. A. Tropp and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Inf. Theory, vol. 53, no. 12, pp. 4655-4666, Dec. 2007.
29. J. Tropp, A. Gilbert, and M. Strauss, "Algorithms for simultaneous sparse approximation part I: Greedy pursuit," Signal Process., vol. 86, no. 3 pp. 572-588, Mar. 2006. (Pubitemid 43106572)
30. L. Xu, C. Lu, Y. Xu, and J. Jia, "Image smoothing via L0 gradient minimiza-tion," ACM Trans. Graph., vol. 30, no. 6, p. 174, Dec. 2011.
31. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, "Image restoration by sparse 3-D transform-domain collaborative filtering," Proc. SPIE, vol. 6812, p. 681207, Mar. 2008.
32. S. Kindermann, S. Osher, and P.W. Jones, "Deblurring and denoising of images by nonlocal functionals," Multiscale Model. Simul., vol. 4, no. 4, pp. 1091-1115, 2005. (Pubitemid 44932284)
33. A. Elmoataz, O. Lezoray, and S. Bougleux, "Nonlocal discrete regularization on weighted graphs: A framework for image and manifold processing," IEEE Trans. Image Process., vol. 17, no. 7, pp. 1047-1060, Jul. 2008.
34. G. Peyré, "Image processing with nonlocal spectral bases," Multiscale Model. Simul., vol. 7, no. 2, pp. 703-730, 2008.
35. X. Zhang, M. Burger, X. Bresson, and S. Osher, "Bregmanized nonlocal regularization for deconvolution and sparse reconstruction," SIAM J. Imag. Sci., vol. 3, no. 3, pp. 253-276, 2010.
36. M. Jung, X. Bresson, T. F. Chan, and L. A. Vese, "Nonlocal Mumford-Shah regularizers for color image restoration," IEEE Trans. Image Process., vol. 20, no. 6, pp. 1583-1598, Jun. 2011.
37. S. Mallat and G. Yu, "Super-resolution with sparse mixing estimators," IEEE Trans. Image Process., vol. 19, no. 11, pp. 2889-2900, Nov. 2010.
38. S. Chen, D. Donoho, and M. Saunders, "Atomic decompositions by basis pursuit," SIAM Rev., vol. 43, no. 1, pp. 129-159, 2001.
39. M. K. Varanasi and B. Aazhang, "Parametric generalized Gaussian density estimation," J. Acoust. Soc. Amer., vol. 86, no. 4, pp. 1404-1415, 1989.
40. C. Chen, E. W. Tramel, and J. E. Fowler, "Compressed-sensing recovery of images and video using multi-hypothesis predictions," in Proc. 45th Asilomar Conf. Signals, Syst., Comput., Pacific Grove, CA, USA, Nov. 2011, pp. 1193-1198.
41. C. Li, W. Yin, H. Jiang, and Y. Zhang, "An efficient augmented Lagrangian method with applications to total variation minimization," Computational Optimization and Applications, Vol. 56, no. 3, pp. 507-530, Dec. 2013.
42. J. Zhang, D. Zhao, C. Zhao, R. Xiong, S. Ma, and W. Gao, "Image compressive sensing recovery via collaborative sparsity," IEEE J. Emerg. Sel. Topics Circuits Syst., vol. 2, no. 3, pp. 380-391, Sep. 2012.
43. T. Goldstein and S. Osher, "The split Bregman algorithm for L1 regularized problems," SIAM J. Imag. Sci., vol. 2, no. 2, pp. 323-343, Apr. 2009.
44. J. Zhang, D. Zhao, R. Xiong, S. Ma, and W. Gao, "Image restoration using joint statistical modeling in space-transform domain," IEEE Trans. Circuits Syst. Video Technol., to be published.
45. L. Zhang, L. Zhang, X. Mou, and D. Zhang, "FSIM: A feature similarity index for image quality assessment," IEEE Trans. Image Process., vol. 20, no. 8, pp. 2378-2386, Aug. 2011.
46. J. Portilla, "Image restoration through L0 analysis-based sparse optimization in tight frames," in Proc. IEEE Int. Conf. Image Process., Nov. 2009, pp. 3909-3912.
47. J. Zhang, D. Zhao, F. Jiang, and W. Gao, "Structural group sparse representation for image compressive sensing recovery," in Proc. IEEE DCC, Snowbird, UT, USA, Mar. 2013, pp. 331-340.
48. M. Zhou et al., "Nonparametric Bayesian dictionary learning for analysis of noisy and incomplete images," IEEE Trans. Image Process., vol. 21, no. 1, pp. 130-144, Jan. 2012.
49. J. Zhang, C. Zhao, D. Zhao, and W. Gao, "Image compressive sensing recovery using adaptively learned sparsifying basis via L0 minimization," Signal Process., vol. 103, pp. 114-126, Oct. 2014.
50. H. Ji, C. Liu, Z. Shen, and Y. Xu, "Robust video denoising using low rank matrix completion," in Proc. IEEE Conf. CVPR, Jun. 2010, pp. 1791-1798.
51. H. Ji, S. Huang, Z. Shen, and Y. Xu, "Robust video restoration by joint sparse and low rank matrix approximation," SIAM J. Imag. Sci., vol. 4, no. 4, pp. 1122-1142, 2011.