Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A FAST LAGRANGE METHOD FOR LARGE-SCALE IMAGE RESTORATION PROBLEMS WITH REFLECTIVE BOUNDARY CONDITION

  • Oh, SeYoung (Department of Mathematics Chungnam National University) ;
  • Kwon, SunJoo (Innovation Center of Engineering Education Chungnam National University)
  • Published : 2012.05.15
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Abstract

The goal of the image restoration is to find a good approximation of the original image for the degraded image, the blurring matrix, and the statistics of the noise vector given. Fast truncated Lagrange (FTL) method has been proposed by G. Landi as a image restoration method for large-scale ill-conditioned BTTB linear systems([3]). We implemented FTL method for the image restoration problem with reflective boundary condition which gives better reconstructions of the unknown, the true image.

Keywords

References

  1. A. Buades, B. Coll, and J. M. Morel, Image Denoising Methods. A New Non- local Principle, SIAM Review 52 (2010), no. 1, 113-147. https://doi.org/10.1137/090773908
  2. R. C. Gonzalez and R. E. Woods, Digital image processing, Prentice Hall, 2002.
  3. G. Landi, A fast truncated Lagrange method for large-scale image restoration problems, Applied Mathematics and Computation 186 (2007), 1075-1082. https://doi.org/10.1016/j.amc.2006.08.039
  4. A. K. Jain, Fundamental of digital image processing, Prentice-Hall, Engelwood Cliffs, NJ 1989.
  5. V. B. Surya Prasath and Arindama Singh, A hybrid convex variational model for image restoration, Applied Mathematics and Computation 215 (2010), 3655-3664. https://doi.org/10.1016/j.amc.2009.11.003
  6. M. K. Ng, R. H. Chan, and W. C. Tang, A fast algorithm for deblurring models with Neumann boundary conditions, SIAM J. Sci. Comp. 21 (1999), no. 3, 851- 866. https://doi.org/10.1137/S1064827598341384
  7. M. K. Ng, W. C. Kwan, Image restoration by cosine transform-based iterative regularization, Applied Mathematics and Computation 160 (2005), 499-515. https://doi.org/10.1016/j.amc.2003.11.017
  8. P. C. Hansen, Regularization Tools, (2001), http://www.imm.dtu.dk/pch.
  9. P. C. Hansen, Deconvolution and Regularization with Toeplitz matrices, Numerical Algorithms, 29 (2002), 323-378. https://doi.org/10.1023/A:1015222829062
  10. P. C. Hansen, J. G. Nagy, and D. P. O'Leary, Deblurring Images Matrices, Spectra, and Filtering, SIAM, 2006.
  11. M. E. Kilmer and D. P. O'Leary, Choosing Regularization Parameters in Iter- ative Methods for Ill-Posed Problems, SIAM J. Matrix Anal. Appl. 22 (2001), 1204-1221. https://doi.org/10.1137/S0895479899345960
  12. K. P. Lee, J. G. Nagy, and L. Perrone, Iterative Methods for Image Restoration: A Matlab Object Oriented Approach, Numerical Algorithms 36 (2004), 73-93. https://doi.org/10.1023/B:NUMA.0000027762.08431.64
  13. S. Serra-Cappizzano, A note on antirefiectibe boundary conditions and fast de- blurring models, SIAM J. Sci. Comp. 25 (1999), no. 4, 851-866.

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