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A fast and robust algorithm for image restoration with periodic boundary conditions

Jingjing Liu North China Electric Power University Yuying Shi North China Electric Power University Yonggui Zhu Communication University of China

Numerical Analysis and Scientific Computing mathscidoc:1702.25078

Journal of Computational Analysis and Applications, 17, (3), 524-538, 2014.3
A new Tikhonov regularization method of Fuhry and Reichel [A new Tikhonov regularization method, Numerical Algorithms, 59:433-445, 2011] exhibits the excellent properties for ill-posed problems, but it can only deal with small or moderate size problems because of the expensive computation of singular value decomposition (SVD). In this paper, we extend the above new Tikhonov regularization method to solve large-scale problems, e.g., image restoration problem with periodic boundary conditions, and realize this extending by applying Fast Fourier Transformation (FFT) algorithm to the spectral decomposition of the block circulant with circulant blocks (BCCB) matrices. Experimental results confirm the superiority of our new method.
Periodic boundary conditions; FFT algorithm; Tikhonov regularization method; Image restoration.
[ Download ] [ 2017-02-10 02:49:57 uploaded by ygzhu ] [ 1496 downloads ] [ 0 comments ] 
@inproceedings{jingjing2014a,
  title={A fast and robust algorithm for image restoration with periodic boundary conditions },
  author={Jingjing Liu, Yuying Shi, and Yonggui Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170210024957115832421},
  booktitle={Journal of Computational Analysis and Applications},
  volume={17},
  number={3},
  pages={524-538},
  year={2014},
}
Jingjing Liu, Yuying Shi, and Yonggui Zhu. A fast and robust algorithm for image restoration with periodic boundary conditions . 2014. Vol. 17. In Journal of Computational Analysis and Applications. pp.524-538. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170210024957115832421.
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