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http://dx.doi.org/10.14403/jcms.2011.24.4.25

TWO DIMENSIONAL VERSION OF LEAST SQUARES METHOD FOR DEBLURRING PROBLEMS  

Kwon, SunJoo (Innovation Center of Engineering Education Chungnam National University)
Oh, SeYoung (Department of Mathematics Chungnam National University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.24, no.4, 2011 , pp. 895-903 More about this Journal
Abstract
A two dimensional version of LSQR iterative algorithm which takes advantages of working solely with the 2-dimensional arrays is developed and applied to the image deblurring problem. The efficiency of the method comparing to the Fourier-based LSQR method and the 2-D version CGLS algorithm methods proposed by Hanson ([4]) is analyzed.
Keywords
image deblurring; Tikhonov regularization; Kronecker product; LSQR method;
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  • Reference
1 A. Bjork, Numerical methods for least squares problems, SIAM, 1996.
2 H. C. Andrews, B. R. Hunt, Digital image restoration, Prentice-Hall Inc, 1977.
3 R. C. Gonzalez and R. E. Woods, Digital image processing, Prentice Hall, 2002.
4 P. C. Hansen, Deconvolution and regularization with Toeplitz matrices, Numerical Algorithm, 29 (2002), 323-328   DOI   ScienceOn
5 P. C. Hansen, J. G. Nagy, and D. P. O' Leary, Deblurring images matrices, spectra, and filtering, SIAM, 2006.
6 P. C. Hansen, Regularization tools 4.0 for Matlab 7.3, Numerical Algorithms 46 (2007), no. 2, 189-194.   DOI   ScienceOn
7 P. C. Hansen, Discrete Inverse Problems: Insight and Algorithms, SIAM, 2010.
8 A. K. Jain, Fundamental of digital image processing, Prentice-Hall, Engelwood Cliffs, NJ, 1989.
9 R. L. Lagendijk, J. Biemond, Iterative identification and restoration of images, Kluwer, 1991.
10 K. P. Lee, J. G. Nagy, and L. Perrone, Iterative methods for image restoration: A Matlab object oriented approach, Numerical Algorithms, 36 (2004), no. 1, 73-93.   DOI
11 C. C. Paige, M. A Saunders, LSQR: An algorithm for sparse Linear equations and sparse least squares, ACM Trans. on Math. Soft. 8 (1982), no. 1, 43-71.   DOI
12 C. R. Vogel, Computational Methods for Inverse Problems, SIAM, 2002.