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

Computer Science and Engineering

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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 language	English (US)
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
State	Published - 2006

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1137/040605436

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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.",

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AB - 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.

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Structured total least squares for color image restoration

Abstract

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