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Preconditioned conjugate gradient method for boundary artifact-free image deblurring
1. | Department of Applied Mathematics, Inje University, Gimhae, Gyeongnam 621-749, South Korea |
2. | Department of Mathematics, Purdue University, West Lafayette, IN47906, United States |
References:
[1] |
F. Aghdasi and R. K. Ward, Reduction of boundary artifacts in image restoration, IEEE Trans. Image Processing, 5 (1996), 611-618.
doi: 10.1109/83.491337. |
[2] |
M. S. C. Almeida and M. A. T. Figueiredo, Frame-based image deblurring with unknown boundary conditions using the alternating direction method of multipliers, in Proceedings of ICIP, (2013), 582-585.
doi: 10.1109/ICIP.2013.6738120. |
[3] |
A. Arićo, M. Donatelli and S. Serra-Capizzano, Spectral analysis of the anti-reflective algebra, Linear Algebra Appl., 428 (2008), 657-675.
doi: 10.1016/j.laa.2007.08.020. |
[4] |
M. Bertalmio, G. Sapiro, V. Caselles and C. Ballester, Image inpainting, SIGGRAPH, (2000), 417-424.
doi: 10.1145/344779.344972. |
[5] |
M. Bertero and P. Boccacci, A simple method for the reduction of boundary effects in the Richardson-Lucy approach to image deconvolution, Astron. Astrophys., 437 (2005), 369-374.
doi: 10.1051/0004-6361:20052717. |
[6] |
D. Calvetti, J. P. Kaipio and E. Someralo, Aristotelian prior boundary conditions, Inter. J. Mathematics and Computer Science, 1 (2006), 63-81. |
[7] |
M. Donatelli, C. Estatico, A. Martinelli and S. Serra-Capizzano, Improved image deblurring with anti-reflective boundary conditions and re-blurring, Inverse Problems, 22 (2006), 2035-2053.
doi: 10.1088/0266-5611/22/6/008. |
[8] |
Y. W. Fan and J. G. Nagy, Synthetic boundary conditions for image deblurring, Linear Algebra Appl., 434 (2011), 2244-2268.
doi: 10.1016/j.laa.2009.12.021. |
[9] |
C. W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Integral Equations of the First Kind, Pitman, Boston, 1984. |
[10] |
M. Hanke and P. C. Hansen, Regularization methods for large-scale problems, Surveys Math. Indust., 3 (1993), 253-315. |
[11] |
M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, Journal of Research of the National Bureau of Standards, 49 (1952), 409-436.
doi: 10.6028/jres.049.044. |
[12] |
A. K. Jain, Fundamentals of Digital Image Processing, Prentice-Hall, Englewood Cliffs, NJ, 1989. |
[13] |
R. Liu and J. Jia, Reducing boundary artifacts in image deconvolution, in Proceedings of ICIP, 2008, 505-508. |
[14] |
L. B. Lucy, An iterative techniques for the rectification of observed distributions, Astronomical Journal, 79 (1974), 745-754.
doi: 10.1086/111605. |
[15] |
M. K. Ng, R. H. Chan and W.-C. Tang, A fast algorithm for deblurring models with Neumann boundary conditions, SIAM J. Sci. Comput., 21 (1999), 851-866.
doi: 10.1137/S1064827598341384. |
[16] |
W. H. Richardson, Bayesian-based iterative method of image restoration, J. Opt. Soc. Am., 62 (1972), 55-59.
doi: 10.1364/JOSA.62.000055. |
[17] |
Y. Saad, Iterative Methods for Sparse Linear Systems, SIAM Publications, Philadelphia, 2003.
doi: 10.1137/1.9780898718003. |
[18] |
S. Serra-Capizzano, A note on anti-reflective boundary conditions and fast deblurring models, SIAM J. Sci. Comput., 25 (2003), 1307-1325.
doi: 10.1137/S1064827502410244. |
[19] |
A. M. Tekalp and M. I. Sezan, Quantitative analysis of artifacts in linear space-invariant image restoration, Multidimensional Syst. Signal Processing, 1 (1990), 143-177.
doi: 10.1007/BF01816547. |
[20] |
R. Vio, J. Bardsley, M. Donatelli and W. Wamsteker, Dealing with edge effects least-squares image deconvolution problems, Astron. Astrophys, 442 (2005), 397-403.
doi: 10.1051/0004-6361:20053414. |
[21] |
J. W. Woods, J. Biemond and A. M. Kekalp, Boundary value problem in image restoration, Proc. Sixth Int. Conf. Acoust. Speech Signal Processing, 10 (1985), 692-695.
doi: 10.1109/ICASSP.1985.1168354. |
show all references
References:
[1] |
F. Aghdasi and R. K. Ward, Reduction of boundary artifacts in image restoration, IEEE Trans. Image Processing, 5 (1996), 611-618.
doi: 10.1109/83.491337. |
[2] |
M. S. C. Almeida and M. A. T. Figueiredo, Frame-based image deblurring with unknown boundary conditions using the alternating direction method of multipliers, in Proceedings of ICIP, (2013), 582-585.
doi: 10.1109/ICIP.2013.6738120. |
[3] |
A. Arićo, M. Donatelli and S. Serra-Capizzano, Spectral analysis of the anti-reflective algebra, Linear Algebra Appl., 428 (2008), 657-675.
doi: 10.1016/j.laa.2007.08.020. |
[4] |
M. Bertalmio, G. Sapiro, V. Caselles and C. Ballester, Image inpainting, SIGGRAPH, (2000), 417-424.
doi: 10.1145/344779.344972. |
[5] |
M. Bertero and P. Boccacci, A simple method for the reduction of boundary effects in the Richardson-Lucy approach to image deconvolution, Astron. Astrophys., 437 (2005), 369-374.
doi: 10.1051/0004-6361:20052717. |
[6] |
D. Calvetti, J. P. Kaipio and E. Someralo, Aristotelian prior boundary conditions, Inter. J. Mathematics and Computer Science, 1 (2006), 63-81. |
[7] |
M. Donatelli, C. Estatico, A. Martinelli and S. Serra-Capizzano, Improved image deblurring with anti-reflective boundary conditions and re-blurring, Inverse Problems, 22 (2006), 2035-2053.
doi: 10.1088/0266-5611/22/6/008. |
[8] |
Y. W. Fan and J. G. Nagy, Synthetic boundary conditions for image deblurring, Linear Algebra Appl., 434 (2011), 2244-2268.
doi: 10.1016/j.laa.2009.12.021. |
[9] |
C. W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Integral Equations of the First Kind, Pitman, Boston, 1984. |
[10] |
M. Hanke and P. C. Hansen, Regularization methods for large-scale problems, Surveys Math. Indust., 3 (1993), 253-315. |
[11] |
M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, Journal of Research of the National Bureau of Standards, 49 (1952), 409-436.
doi: 10.6028/jres.049.044. |
[12] |
A. K. Jain, Fundamentals of Digital Image Processing, Prentice-Hall, Englewood Cliffs, NJ, 1989. |
[13] |
R. Liu and J. Jia, Reducing boundary artifacts in image deconvolution, in Proceedings of ICIP, 2008, 505-508. |
[14] |
L. B. Lucy, An iterative techniques for the rectification of observed distributions, Astronomical Journal, 79 (1974), 745-754.
doi: 10.1086/111605. |
[15] |
M. K. Ng, R. H. Chan and W.-C. Tang, A fast algorithm for deblurring models with Neumann boundary conditions, SIAM J. Sci. Comput., 21 (1999), 851-866.
doi: 10.1137/S1064827598341384. |
[16] |
W. H. Richardson, Bayesian-based iterative method of image restoration, J. Opt. Soc. Am., 62 (1972), 55-59.
doi: 10.1364/JOSA.62.000055. |
[17] |
Y. Saad, Iterative Methods for Sparse Linear Systems, SIAM Publications, Philadelphia, 2003.
doi: 10.1137/1.9780898718003. |
[18] |
S. Serra-Capizzano, A note on anti-reflective boundary conditions and fast deblurring models, SIAM J. Sci. Comput., 25 (2003), 1307-1325.
doi: 10.1137/S1064827502410244. |
[19] |
A. M. Tekalp and M. I. Sezan, Quantitative analysis of artifacts in linear space-invariant image restoration, Multidimensional Syst. Signal Processing, 1 (1990), 143-177.
doi: 10.1007/BF01816547. |
[20] |
R. Vio, J. Bardsley, M. Donatelli and W. Wamsteker, Dealing with edge effects least-squares image deconvolution problems, Astron. Astrophys, 442 (2005), 397-403.
doi: 10.1051/0004-6361:20053414. |
[21] |
J. W. Woods, J. Biemond and A. M. Kekalp, Boundary value problem in image restoration, Proc. Sixth Int. Conf. Acoust. Speech Signal Processing, 10 (1985), 692-695.
doi: 10.1109/ICASSP.1985.1168354. |
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