Regularizing active set method for nonnegatively constrained ill-posed multichannel image restoration problem

Applied Optics

Volumn 48, Issue 7, 2009, Pages 1389-1401

  Wang, Yanfei ^a   Cao, Jingjie ^a   Yuan, Yaxiang ^b   Yang, Changchun ^a   Xiu, Naihua ^c  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

^c BEIJING JIAOTONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CONJUGATE GRADIENT METHOD; IMAGE RECONSTRUCTION; NUMBER THEORY; NUMERICAL METHODS; QUADRATIC PROGRAMMING; RESTORATION;

ACTIVE SET METHODS; BLURRED IMAGE RESTORATIONS; IMAGE DEBLURRING PROBLEMS; MULTICHANNEL IMAGE RESTORATION; MULTICHANNEL IMAGES; NON-NEGATIVITY CONSTRAINTS; NUMERICAL EXPERIMENTS; SOLUTION TECHNIQUES;

IMAGE ENHANCEMENT;

EID: 63049117846     PISSN: 1559128X     EISSN: 15394522     Source Type: Journal    
DOI: 10.1364/AO.48.001389     Document Type: Article

References (50)

1. G. Angelopoulos and I. Pitas, "Multichannel Wiener filters in color image restoration," IEEE Trans. Circuits Syst. Video Technol. 4, 83-87 (1994).
2. D. L. Angwin and H. Haufman, "Effects of modeling domains on recursive color image restoration," in IEEE Trans. Acoust., Speech, Signal Process. 12, 1229-1231 (1987).
3. A. Beck, A. Ben, and Y. C. Eldar, "Robust mean-squared error estimation of multiple signals in linear systems affected by model and noise uncertainties," Math. Program. 107, 155-187 (2006).
4. J. Bescos, J. H. Altamirano, A. Santisteban, and J. Santamaria, "Digital restoration models for color imaging," Appl. Opt. 27, 419-425 (1988).
5. T. W. S. Chow, X. D. Li, and K.-T. Ng, "Double-regularization approach for blind restoration of multichannel imagery," IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48, 1075-1085 (2001).
6. Y. C. Eldar, A. Ben-Tal, and A. Nemirovski, "Robust meansquared error estimation in the presence of model uncertainties," IEEE Trans. Signal Process. 53, 168-181 (ISPRS Working Groups WG VII/1, 2005).
7. N. P. Galatsanos and R. T. Chin, "Digital restoration of multi-channel images," IEEE Trans. Acoust., Speech Signal Process. 37, 415-421 (1989).
8. N. P. Galatsanos and R. T. Chin, "Restoration of color images by multichannel Kalman filtering," IEEE Trans. Signal Process. 39, 2237-2252 (1991).
9. N. P. Galatsanos, A. K. Katsaggelos, R. T. Chin, and A. D. Hillery, "Least squares restoration of multichannel images," IEEE Trans. Signal Process. 39, 2222-2236 (1991).
10. M.-C. Hong, T. Stathaki, and A. K. Katsasggelos, "Iterative regularized least-mean mixed-norm image restoration," Opt. Eng. 41, 2525-2524 (2002).
11. M.-C. Hong, T. Stathaki, and A. K. Katsasggelos, "Iterative regularized mixed norm multichannel image restoration," J. Electron. Imaging 14, 013004 (2005).
12. B. R. Hunt and O. Kubler, "Karhunen-Loeve multispectral image restoration, part I: theory," IEEE Trans. Acoust., Speech Signal Process. ASSP-32, 592-600 (1984).
13. A. K. Katsaggelos and J. K Paik, "Iterative color image restoration algorithms," IEEE Trans. Acoust., Speech Signal Process. 2, 1028-1031 (1988).
14. N. Ohyama, M. Yachida, E. Badique, J. Tsujiuchi, and T Honda, "Least-squares filter for color-image restoration," J. Opt. Soc. Am. A 5, 19-24 (1988).
15. R. R. Schultz and R. L. Stevenson, "Stochastic modeling and estimation of multispectral image data," IEEE Trans. Image Process. 4, 1109-1119 (1995).
16. M. A. Sezan and H. J. Trussell, "Use of a priori knowledge in multispectral image restoration," in IEEE Trans. Acoust., Speech Signal Process. 3, 1429-1432 (1989).
17. A. M. Tekalp and G. Pavlovic, "Space-variant and color image restoration using Kalman filtering," in Multidimensional Signal Processing Workshop, Vol. 6 (IEEE, 1989), pp. 186-187
18. W. W. Zhu, Nikolas P. Galatsanos, and A. K. Katsaggelos, "Regularized multichannel image restoration using cross-validation," Graphical Models 57, 345-356 (1995).
19. Y. F. Wang, X. W. Li, S. Q. Ma, H. Yang, Z. Nashed, and Y. N. Guan, "BRDF model inversion of multiangular remote sensing: ill-posedness and interior point solution method," in Proceedings of the 9th International Symposium on Physical Measurements and Signature in Remote Sensing (ISPMSRS) (ISPRS Working Groups WG VII/1, 2005), Vol. XXXVI, pp. 328-330.
20. Y. F. Wang, S. Q. Ma, H. Yang, J. D. Wang, and X. W. Li, "On the effective inversion by imposing a priori information for retrieval of land surface parameters," Sci. China (Ser. D) 52, 1-10 (2009).
21. H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, 1996).
22. T. Y. Xiao, Sh. G. Yu, and Y. F. Wang, Numerical Methods for the Solution of Inverse Problems (Beijing: Science Press, 2003).
23. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D (Amsterdam) 60, 259-268 (1992).
24. C. R. Vogel and M. E. Oman, "A fast, robust algorithm for total variation based reconstruction of noisy, blurred images," IEEE Trans. Image Process. 7, 813-824 (1998).
25. P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (Society for Industrial and Applied Mathematics, 1998).
26. C. R. Vogel, Computational Methods for Inverse Problems (Society for Applied and Industrial Mathematics, 2002).
27. R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and Vorst H. Van der, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Applied and Industrial Mathematics, 1994).
28. Y. F. Wang and S. Q. Ma, "Projected Barzilai-Borwein method for large scale nonnegative image restoration," Inverse Probl. Sci. Eng. 15, 559-583 (2007).
29. M. Hanke and J. Nagy, "Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques," Inverse Probl. 12, 157-173 (1996).
30. Y. F. Wang, "On the regularity of trust region-CG algorithm: with application to image deconvolution problem," Sci. China Ser. A Math., Phys., Astron. 46, 312-325 (2003).
31. Z. W. Wen and Y. F. Wang, " A new trust region algorithm for image restoration," Sci. China Ser. A Math., Phys., Astron. 48, 169-184 (2005).
32. Y. F. Wang and Y. Yuan, "Convergence and regularity of trust region methods for nonlinear ill-posed inverse problems," Inverse Probl. 21, 821-838 (2005).
33. J. Bardsley and C. R. Vogel, "A nonnegatively constrained convex programming method for image reconstruction," SIAM J. Sci. Comput. 25, 1326-1343 (2004).
34. M. Hanke, J. Nagy, and C. R. Vogel, "Quasi-Newton approach to nonnegative image restorations," Numer. Linear Algebra Appl. 316, 223-236 (2000).
35. J. Nagy and Z. Strakos, "Enforcing nonnegativity in image reconstruction algorithms," Proc. SPIE 4121, 182-190 (2000).
36. M. Rojas and T. Steihaug, "An interior-point trust-region-based method for large-scale nonnegative regularization," CERFACS Tech. Rep. TR/PA/01/11 (Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique, 2002).
37. R. Fletcher, Practical Methods of Optimization, 2nd ed. (Wiley, 1987).
38. J. Nocedal and S. J. Wright, Numerical Optimization (Springer-Verlag, 1999).
39. Y. X. Yuan, Numerical Methods for Nonlinear Programming (Shanghai Science and Technology Publication, 1993).
40. Y. F. Wang and C. C. Yang, "A regularizing active set method for retrieval of atmospheric aerosol particle size distribution function," J. Opt. Soc. Am. A 25, 348-356 (2008).
41. Y. X. Yuan, "Subspace techniques for nonlinear optimization," in Some Topics in Industrial and Applied Mathematics, R. Jeltsch, D. Q. Li, and I. H. Sloan, eds., Series in Contemporary Applied Mathematics CAM 8 (Higher Education Press, (2007), pp. 206-218.
42. J. J. More and G. Toraldo, "On the solution of large quadratic programming problems with bound constraints," SIAM J. Control Optim. 1, 93-113 (1991).
43. D. P. O'Leary, "A generalized conjugate gradient algorithm for solving a class of quadratic programming problems," Numer. Linear Algebra Appl. 34, 371-399 (1980).
44. D. P Bertsekas, "Projected Newton methods for optimization problems with simple constraints," SIAM J. Control Optim. 20, 221-246 (1982).
45. A. Bakushinsky and A. Goncharsky, Ill-Posed Problems: Theory and Applications (Kluwer Academic, 1994).
46. Y. F. Wang, Computational Methods for Inverse Problems and Their Applications (Higher Education Press, 2007).
47. Y. F. Wang, S. F. Fan, and X. Feng, "Retrieval of the aerosol particle size distribution function by incorporating a priori information," J. Aerosol Sci. 38 885-901 (2007).
48. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, 1998).
49. Y. X. Yuan and W. Y. Sun, Theory and Methods for Optimization (Science Press, 1997).
50. D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory 52, 1289-1306 (2006).