Selection of regularization parameter in total variation image restoration

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 26, Issue 11, 2009, Pages 2311-2320

  Liao, Haiyong ^a   Li, Fang ^b   Ng, Michael K ^a  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b EAST CHINA NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE RECONSTRUCTION; MATLAB;

AUTOMATIC SELECTION; BLURRED AND NOISY IMAGES; COMPUTING ENVIRONMENTS; DISCREPANCY PRINCIPLE; GENERALIZED CROSS VALIDATION; GENERALIZED CROSS VALIDATION METHOD; IMAGE RESTORATION; REGULARIZATION PARAMETERS; RESTORE IMAGE; SELECTION METHODS; TIKHONOV REGULARIZATION; TOTAL VARIATION; TV IMAGE; VISUAL QUALITIES;

RESTORATION;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; COMPUTER; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; INFORMATION PROCESSING; METHODOLOGY; NORMAL DISTRIBUTION; OPTICS; STATISTICAL MODEL; THEORETICAL MODEL;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER SIMULATION; COMPUTERS; DATA COMPRESSION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MODELS, STATISTICAL; MODELS, THEORETICAL; NORMAL DISTRIBUTION; OPTICS AND PHOTONICS; PATTERN RECOGNITION, AUTOMATED;

EID: 70449721128     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.26.002311     Document Type: Article

References (42)

1. J. M. Morel and S. Solimini, Variational Methods for Image Segmentation (Birkhauser, 1995).
2. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D 60, 259-268 (1992).
3. C. Vogel and M. Oman, "Iterative method for total variation denoising," SIAM J. Sci. Comput. (USA) 17, 227-238 (1996).
4. G. Bellettini, V. Caselles, and M. Novaga, "The total variation flow in RN," J. Differ. Equations 184, 475-525 (2002).
5. A. Chambolle and P.-L. Lions, "Image recovery via total variation minimization and related problems," Numer. Math. 76, 167-188 (1997).
6. D. Dobson and F. Santosa, "Reovery of blocky images from noisy and blurred data," SIAM J. Appl. Math. 56, 1181-1198 (1996).
7. D. Strong and T. Chan, "Edge-preserving and scaledependent properties of total variation regularization," Inverse Probl. 19, 165-187 (2003).
8. P. Blomgren and T. Chan, "Color TV: total variation methods for restoration of vector-valued images," IEEE Trans. Image Process. 7, 304-309 (1998).
9. T. Chan, M. Ng, A. Yau, and A. Yip, "Superresolution image reconstruction using fast inpainting algorithms," Appl. Comput. Harmonic Anal. 23, 3-24 (2007).
10. T. Chan and C. Wong, "Total variation blind deconvolution," IEEE Trans. Image Process. 7, 370-375 (1998).
11. T. Chan and J. Shen, "Variational restoration of nonflat image features: models and algorithms," SIAM J. Appl. Math. 61, 1338-1361 (2001).
12. N. Paragios, Y. Chen, and O. Faugeras, Handbook of Mathematical Models in Computer Vision (Springer, 2006).
13. D. Krishnan, P. Lin, and X. Tai, "An efficient operator splitting method for noise removal in images," Commun. Comput. Phys. 1, 847-858 (2006).
14. M. Lysaker and X. Tai, "Noise removal using smoothed normals and surface fitting," IEEE Trans. Image Process. 13, 1345-1357 (2004).
15. M. Hintermüller and K. Kunisch, "Total bounded variation regularization as a bilaterally constrained optimization problem," SIAM J. Appl. Math. 64, 1311-1333 (2004).
16. M. Hintermüller and G. Stadler, "An infesible primal-dual algorithm for total bounded variation-based infconvolution-type image restoration," SIAM J. Sci. Comput. (USA) 28, 1-23 (2006).
17. T. Chan, G. Golub, and P. Mulet, "A nonlinear primal-dual method for total variation-based image restoration," SIAM J. Sci. Comput. (USA) 20, 1964-1977 (1999).
18. M. Hintermüller, K. Ito, and K. Kunisch, "The primal-dual active set strategy as a semismooth Newton's method," SIAM J. Optim. 13, 865-888 (2003).
19. Y. Li and F. Santosa, "A computational algorithm for minimizing total variation in image reconstruction," IEEE Trans. Image Process. 5, 987-995 (1996).
20. H. Fu, M. Ng, M. Nikolova, and J. Barlow, "Efficient minimization methods of mixed 11-11 and 12-11 norms for image restoration," SIAM J. Sci. Comput. (USA) 27, 1881-1902 (2006).
21. Y. Huang, M. Ng, and Y. Wen, "A fast total variation minimization method for image restoration," SIAM J. Multiscale Model. Simul. 7, 774-795 (2008).
22. X. Guo, F. Li, and M. Ng, "A fast l1-TV algorithm for image restoration," SIAM J. Sci. Comput. (USA) (to be published).
23. Y. Wang, J. Yang, W. Yin, and Y. Zhang, "A new alternating minimization algorithm for total variation image reconstruction," SIAM J. Imaging Sci. 1, 248-272 (2008).
24. J. Yang, W. Yin, Y. Zhang, and Y. Wang, "A fast algorithm for edge-preserving variational multichannel image restoration," SIAM J. Imaging Sci. 2, 569-592 (2008).
25. R. Gonzalez and R. Woods, Digital Image Processing (Addison Wesley, 1992).
26. H. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, 1996).
27. P. Hansen, Rank-Deficient and Discrete Ill-Posed Problems (SIAM, 1998).
28. G. Golub, M. Heath, and G. Wahba, "Generalized crossvalidation as a method for choosing a good ridge parameter," Technometrics 21, 215-223 (1979).
29. P. Hansen, J. Nagy, and D. O'leary, Deblurring Images: Matrices, Spectra, and Filtering (SIAM, 2006).
30. P. Hansen and D. O'Leary, "The use of the L-curve in the regularization of discrete ill-posed problems," SIAM J. Sci. Comput. (USA) 14, 1487-1503 (1993).
31. C. Vogel, Computational Methods for Inverse Problems (SIAM, 1998).
32. Y. Lin and B. Wohlberg, "Application of the UPRE method to optimal parameter selection for large scale regularization problems," in Proceedings of the IEEE Southwest Symposium on Image Analysis and Interpretation (IEEE, 2008), pp. 89-92.
33. S. D. Babacan, R. Molina, and A. K. Katsaggelos, "Parameter estimation in TV image restoration using variation distribution approximation," IEEE Trans. Image Process. 17, 326-339 (2008).
34. R. Molina, J. Mateos, and A. Katsaggelos, "Blind deconvolution using a variational approach to parameter, image and blur estimation," IEEE Trans. Image Process. 15, 3715-3727 (2006).
35. M. Ng, Iterative Methods for Toeplitz Systems (Oxford Univ. Press, 2004).
36. A. Chambolle, "An algorithm for total variation minimization and applications," J. Math. Imaging Vision 20, 89-97 (2004).
37. M. Ng, L. Qi, Y. Yang, and Y. Huang, "On semismooth Newton's methods for total variation minimization," J. Math. Imaging Vision 27, 265-276 (2007).
38. G. Golub and U. Matt, "Generalized cross-validation for large scale problems," J. Comput. Graph. Stat. 6, 1-34 (1997).
39. M. Ng, R. Chan, and W. Tang, "A fast algorithm for deblurring models with Neumann boundary conditions," SIAM J. Sci. Comput. 21, 851-866 (2000).
40. G. Golub and G. Meurant, "Matrices, moments and quadrature," in Numerical Analysis, D. Griffiths and G. Watson, eds. (Longman, 1994), pp. 105-156.
41. L. Reichel and H. Sadok, "A new L-curve for ill-posed problems," J. Comput. Appl. Math. 219, 493-508 (2008).
42. L. Reichel, H. Sadok, and A. Shyshkov, "Greedy Tikhonov regularization for large linear ill-posed problems," Int. J. Comput. Math. 84, 1151-1166 (2007). (Pubitemid 47341073)