Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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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)
  • Received : 2011.10.15
  • Accepted : 2011.11.18
  • Published : 2011.12.30
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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.

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References

  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 https://doi.org/10.1023/A:1015222829062
  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. https://doi.org/10.1007/s11075-007-9136-9
  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. https://doi.org/10.1023/B:NUMA.0000027762.08431.64
  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. https://doi.org/10.1145/355984.355989
  12. C. R. Vogel, Computational Methods for Inverse Problems, SIAM, 2002.