Structured Total Least Squares for Color Image Restoration

Haoying Fu; Michael K. Ng; Jesse L. Barlow

doi:10.1137/040605436

Structured Total Least Squares for Color Image Restoration

Haoying Fu, Michael K. Ng, Jesse L. Barlow

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

10 Citations (Scopus)

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Abstract

The problem of 3 x 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 language	English
Pages (from-to)	1100-1119
Number of pages	20
Journal	SIAM Journal on Scientific Computing
Volume	28
Issue number	3
DOIs	https://doi.org/10.1137/040605436
Publication status	Published - 4 Aug 2006

Scopus Subject Areas

Computational Mathematics
Applied Mathematics

User-Defined Keywords

structured total least squares
color image
image restoration
Toeplitz-like matrices
preconditioners

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title = "Structured Total Least Squares for Color Image Restoration",

abstract = "The problem of 3 x 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.",

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author = "Haoying Fu and Ng, {Michael K.} and Barlow, {Jesse L.}",

note = "Funding information: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (mng@ math.hkbu.edu.hk). The research of this author was supported in part by Hong Kong Research Grants Council grants 7046/03P, 7035/04P, and 7035/05P and HKBU FRGs. Publisher copyright: Copyright {\textcopyright} 2006 Society for Industrial and Applied Mathematics",

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AU - Ng, Michael K.

AU - Barlow, Jesse L.

N1 - Funding information: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (mng@ math.hkbu.edu.hk). The research of this author was supported in part by Hong Kong Research Grants Council grants 7046/03P, 7035/04P, and 7035/05P and HKBU FRGs. Publisher copyright: Copyright © 2006 Society for Industrial and Applied Mathematics

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N2 - The problem of 3 x 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.

AB - The problem of 3 x 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.

KW - structured total least squares

KW - color image

KW - image restoration

KW - Toeplitz-like matrices

KW - preconditioners

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JO - SIAM Journal on Scientific Computing

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Structured Total Least Squares for Color Image Restoration

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