Kronecker product approximations for image restoration with whole-sample symmetric boundary conditions

Information Sciences

Volumn 186, Issue 1, 2012, Pages 150-163

  Lv, Xiao Guang ^a   Huang, Ting Zhu ^a   Xu, Zong Ben ^b   Zhao, Xi Le ^a  

^a UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

GCV; Image restoration; Kronecker product approximation; TSVD; Whole sample symmetric BCs

Indexed keywords

FAST ALGORITHMS; GCV; KRONECKER PRODUCT; MATRIX; POINT-SPREAD FUNCTION; RESTORE IMAGE; RESULTS REPORTING; SIGNAL AND IMAGE PROCESSING; SUB-MATRICES; TSVD; WHOLE-SAMPLE SYMMETRIC BCS;

BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; IMAGE RECONSTRUCTION; OPTICAL TRANSFER FUNCTION; RESTORATION;

APPROXIMATION ALGORITHMS;

EID: 81355160241     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2011.09.026     Document Type: Article

References (50)

1. F. Aghdasi, and R. Ward Reduction of boundary artifacts in image restoration IEEE Trans. Image Process. 5 4 1996 611 618 (Pubitemid 126777660)
2. H. Andrew, and B. Hunt Digital Image Restoration 1977 Prentice-Hall Englewood Cliffs, NJ
3. M. Banham, and A. Katsaggelos Digital image restoration IEEE Signal Process. Mag. 14 2 1997 24 41 (Pubitemid 127571670)
4. S. Bonettini, and V. Ruggiero An alternating extragradient method for total variation-based image restoration from Poisson data Inverse Probl. 27 2011 095001 26 pp
5. K. Boukerrou, and L. Kurz Suppression of "salt and pepper" noise based on Youden designs Inform. Sci. 110 1998 217 235 (Pubitemid 128674962)
6. J.F. Cai, S. Osher, and Z.W. Shen Split Bregman methods and frame based image restoration Multiscale Model. Simul. 8 2 2010 337 369
7. S.S. Capizzano A note on anti-reflective boundary conditions and fast deblurring models SIAM J. Sci. Comput. 25 2003 1307 1325
8. T.F. Chan, and J. Shen Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods 2005 SIAM Philadelphia
9. F. Chen, L. Yu, Image deblurring with odd symmetry discrete Neumann boundary condition, in: Proceedings of the Sixth International Conference on Machine Learning and Cybernetics, Hong Kong, 2007.
10. M. Christiansen, and M. Hanke Deblurring methods using antireflective boundary conditions SIAM J. Sci. Comput. 30 2 2008 855 872
11. J. Chung, and J.G. Nagy An efficient iterative approach for large-scale separable nonlinear inverse problems SIAM J. Sci. Comput. 31 6 2010 4654 4674
12. M. Donatelli, and S.S. Capizzano Anti-reflective boundary conditions and re-blurring Inverse Probl. 21 2005 169 182 (Pubitemid 40238421)
13. Y. Dong, M. Hintermüller, and M.M. Rincon-Camacho Automated regularization parameter selection in multi-scale total variation models for image restoration J. Math. Imaging Vis. 40 2011 82 104
14. E. Dowski, and W. Cathey Extended depth of field through wavefront coding Appl. Optics 34 1995 1859 1866
15. H. Engl, M. Hanke, and A. Neubauer Regularization of Inverse Problems 1996 Kluwer Academic Publishers The Netherlands
16. Y.W. Fan, and J.G. Nagy Synthetic boundary conditions for image deblurring Linear Algebra Appl. 434 11 2011 2244 2268
17. A.I. González, M. Graña, J.R. Cabello, A. D'Anjou, and F.X. Albizuri Experimental results of an evolution-based adaptation strategy for VQ image filtering Inform. Sci. 176 2006 2988 3010
18. A.E. Hamidi, M. Ménard, M. Lugiez, and C. Ghannam Weighted and extended total variation for image restoration and decomposition Pattern Recognit. 43 2010 1564 1576
19. M. Hanke, J.G. Nagy, and C.R. Vogel Quasi-Newton approach to nonnegative image restorations Linear Algebra Appl. 316 2000 223 236
20. P.C. Hansen Rank Defficient and Discrete Ill-posed Problems: Numerical Aspects of Linear Inversion 1997 SIAM Philadelphia
21. P.C. Hansen, J.G. Nagy, and D.P. O'Leary Deblurring Images: Matrices, Spectra, and Filtering 2006 SIAM Philadelphia
22. P.C. Hansen Discrete Inverse Problems: Insight and Algorithms 2010 SIAM Philadelphia
23. G. Jeon, M. Anisetti, V. Bellandi, E. Damiani, and J. Jeong Designing of a type-2 fuzzy logic filter for improving edge-preserving restoration of interlaced-to-progressive conversion Inform. Sci. 179 13 2009 2194 2207
24. J. Kamm, Singular value decomposition-based methods for signal and image processing, Ph. D. Thesis, Southern Methodist University, USA, 1998.
25. J. Kamm, and J.G. Nagy Optimal Kronecker product approximation of block Toeplitz matrices SIAM J. Matrix Analysis Appl. 22 2000 155 172 (Pubitemid 33229424)
26. R.L. Lagendijk, J. Biemond, and D.E. Boekee Identification and restoration of noisy blurred images using the expectation-maximization algorithm IEEE Trans. Acoust. Speech Signal Process. 38 7 1990 1180 1191 (Pubitemid 20726262)
27. K.T. Lay, and A.K. Katsaggelos Identification and restoration based on the expectation-maximization algorithm Opt. Eng. 29 5 1990 436 445 (Pubitemid 20717537)
28. X. Li Fine-granularity and spatially-adaptive regularization for projection-based image deblurring IEEE Trans. Image Process. 20 4 2011 971 983
29. C.L. Lim, B. Honarvar, K.H. Thung, and R. Paramesran Fast computation of exact Zernike moments using cascaded digital filters Inform. Sci. 181 17 2011 3638 3651
30. T.C. Lin A new adaptive center weighted median filter for suppressing impulsive noise in images Inform. Sci. 177 2007 1073 1087
31. T.C. Lin Switching-based filter based on Dempsters combination rule for image processing Inform. Sci. 180 2010 4892 4908
32. C.F.V. Loan, and N.P. Pitsianis Approximation with Kronecker products Moonen MS, Golub GH, Linear Algebra for Large Scale and Real Time Applications 1993 Kluwer Dordrecht 293 314
33. S. Martucci Symmetric convolution and the discrete sine and cosine transforms IEEE Trans. Signal Process. 42 1994 1038 1051
34. O.V. Michailovich An iterative shrinkage approach to total-variation image restoration IEEE Trans. Image Process. 20 5 2011 1281 1299
35. J.G. Nagy, M.K. Ng, and L. Perrone Kronecker product approximations for image restoration with reflexive boundary conditions SIAM J. Matrix Anal. Appl. 25 2003 829 841 (Pubitemid 38920234)
36. J.G. Nagy, K. Palmer, and L. Perrone Iterative methods for image deblurring: a Matlab object-oriented approach Numer. Algor. 36 2004 73 93 (Pubitemid 39072750)
37. M.K. Ng, R. Chan, and W. Tang A fast algorithm for deblurring models with Neumann boundary conditions SIAM J. Sci. Comput. 21 2000 851 866
38. M.K. Ng, P. Weiss, and X. Yuan Solving constrained total-variation image restoration and reconstruction problems via alternating direction methods SIAM J. Sci. Comput. 32 5 2010 2710 2736
39. H. Nobuhara, B. Bede, and K. Hirota On various eigen fuzzy sets and their application to image reconstruction Inform. Sci. 176 2006 2988 3010 (Pubitemid 44066379)
40. Z. Pang, and Y. Yang A projected gradient algorithm based on the augmented Lagrangian strategy for image restoration and texture extraction Image Vision Comput. 29 2011 117 126
41. L. Perrone Kronecker product approximations for image restoration with anti-reflective boundary conditions Numer. Lin. Alg. Appl. 13 2006 1 22 (Pubitemid 43171466)
42. N.P. Pitsianis, The Kronecker product in approximation and fast transform generation, Ph. D. Thesis, Cornell University, Ithaca, NY, 1997.
43. S.J. Reeves, and R.M. Mersereau Blur identification by the method of generalized cross-validation IEEE Trans. Image Process. 1 7 1992 301 311
44. M. Rojas, and T. Steihaug An interior-point trust-region-based method for large-scale non-negative regularization Inverse Probl. 18 2002 1291 1307 (Pubitemid 35208368)
45. E. Shaked, and O. Michailovich Iterative shrinkage approach to restoration of optical imagery IEEE Trans. Image Process. 20 2 2011 405 416
46. V.N. Strakhov, and S.V. Vorontsov Digital image deblurring with SOR Inverse Probl. 24 2 2008 p.02502 10.1088/0266-5611/24/2/025024 (Pubitemid 351591138)
47. G. Strang The discrete cosine transform SIAM Rev. 41 1999 135 147 (Pubitemid 129723752)
48. C.R. Vogel Computational Methods for Inverse Problems 2002 SIAM Philadelphia
49. Z. Wang, and A.C. Bovik Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures IEEE Signal Process. Mag. 26 1 2009 98 117
50. W. Zhang, Z. Ye, T. Zhao, Y. Chen, and F. Yu Point spread function characteristics analysis of the wavefront coding system Optics Exp. 15 4 2007 1543 1552