Structured total least squares for color image restoration

Haoying Fu*, Kwok Po NG, Jesse L. Barlow

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

The problem of 3 × 3 color mixing image restoration is considered. The blurring matrices, as well as the observed image, are contaminated by noise; therefore the total least squares (TLS) method is employed to restore the original image. Since the blurring matrices are also structured, we apply the structured total least squares (STLS) method [J. B. Rosen, H. Park, and J. Glick, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 110-126]. The blurring matrices are generally ill conditioned; thus Tikhonov's regularization is used to stabilize the solution. Since Neumann boundary conditions are used in the restoration process, the discrete cosine transform (DCT) based preconditioner is effective for the linear systems encountered in our STLS algorithm.

Original languageEnglish
Pages (from-to)1100-1119
Number of pages20
JournalSIAM Journal of Scientific Computing
Volume28
Issue number3
DOIs
Publication statusPublished - 2006

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Color image
  • Image restoration
  • Preconditioners
  • Structured total least squares
  • Toeplitz-like matrices

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