A method for structured linear total least norm on blind deconvolution problem

  • SeYoung Oh
  • SunJoo Kwon
  • Jae Heon Yun


The regularized structured total least norm (RSTLN) method finds an approximate solutionx and error matrixE to the overdetermined linear system (H+E)x≈b, preserving structure ofH. A new separation scheme by parts of variables for the regularized structured total least norm on blind deconvolution problem is suggested. A method combining the regularized structured total least norm method with a separation by parts of variables can be obtain a better approximated solution and a smaller residual. Computational results for the practical problem with Block Toeplitz with Toeplitz Block structure show the new method ensures more efficiency on image restoration.

AMS Mathematics Subject Classification

65F22 65K10 

Key words and phrases

Blind deconvolution image restoration regularized structured total least norm residual reduction 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. H. Golub and C. F. Van Loan,An analysis of the total least squares problem, SIAM J. Numer. Anal.,17(6) (1980), 883–893.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    R. C. Gonzalez and R. E. Woods,Digital Image Processing, Prentice Hall, (2002)Google Scholar
  3. 3.
    P. C. Hansen,Deconvolution and Regularization with Toeplitz matrices, Numerical Algorithms29 (2002), 323–378.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    P. C. Hansen,Regularization Tools, (2001), Scholar
  5. 5.
    P. C. Hansen,Rank-Deficient and Discrete ill-posed problems, SIAM, 1998.Google Scholar
  6. 6.
    M. E. Kilmer and D. P. O'Leary,Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems, SIAM J. Matrix Anal. Appl.22 (2001), 1204–1221.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    S. J. Kwon,A Hybrid Method for Regularized Structured Linear Total Least Norm, J. Appl. Math. & Computing,18 (1–2) (2005), 621–637.Google Scholar
  8. 8.
    K. P. Lee, J. G. Nagy and L. Perrone,Iterative Methods for Image Restoration: A Matlab Object Oriented Approach, Numerical Algorithms,36 (1) (2004), 73–93.CrossRefMathSciNetGoogle Scholar
  9. 9.
    A. Pruessner and D. P. O'LEARY:Blind deconvolution using a regularized structured total least norm algorithms, SIAM J. Matrix Anal. Appl.24 (4) (2003), 1018–1037.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    J. B. Rosen, H. Park and J. Glick,Total Least Norm Formulation and Solution for Structured Problems, SIAM J. Matrix Anal. Appl.,17 (1) (1996), 110–126.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2005

Authors and Affiliations

  1. 1.Department of MathematicsChungnam National UniversityDaejeonKorea
  2. 2.Department of Mathematics, Institute for Basic Sciences & College of Natural SciencesChungbuk National UniversityCheongjuKorea

Personalised recommendations