An iterative regularized mixed-norm image restoration algorithm

Min Cheol Hong; Tania Stathaki; Aggelos K. Katsaggelos

doi:10.1117/12.298374

An iterative regularized mixed-norm image restoration algorithm

Min Cheol Hong^*, Tania Stathaki, Aggelos K. Katsaggelos

^*Corresponding author for this work

MRC - Materials Research Center

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

1 Scopus citations

Abstract

This paper introduces a regularized mixed-norm image restoration algorithm. A functional which combines the least mean squares (LMS), the least mean fourth (LMF), and a smoothing functional is proposed. A function of the kurtosis is used to determine the relative importance between the LMS and the LMF functionals, and a function of the previous two functionals and the smoothing functionals is utilized for determining the regularization parameter. The two parameters are chosen in such a way that the proposed functional is convex, so that a local minimizer becomes a global minimizer. The novelty of the proposed algorithm is that no knowledge of the noise distribution is required, and the relative contribution of the LMS, the LMF and the smoothing functionals is adjusted based on the partially restored image.

Original language	English (US)
Pages (from-to)	603-614
Number of pages	12
Journal	Proceedings of SPIE - The International Society for Optical Engineering
Volume	3309
Issue number	2
DOIs	https://doi.org/10.1117/12.298374
State	Published - 1998
Event	Visual Communications and Image Processing '98 - San Jose, CA, United States Duration: Jan 28 1998 → Jan 30 1998

Keywords

Kurtosis
Mixed-norms
Regularized image restoration
Smoothing functional

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Condensed Matter Physics
Computer Science Applications
Applied Mathematics
Electrical and Electronic Engineering

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10.1117/12.298374

Cite this

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title = "An iterative regularized mixed-norm image restoration algorithm",

abstract = "This paper introduces a regularized mixed-norm image restoration algorithm. A functional which combines the least mean squares (LMS), the least mean fourth (LMF), and a smoothing functional is proposed. A function of the kurtosis is used to determine the relative importance between the LMS and the LMF functionals, and a function of the previous two functionals and the smoothing functionals is utilized for determining the regularization parameter. The two parameters are chosen in such a way that the proposed functional is convex, so that a local minimizer becomes a global minimizer. The novelty of the proposed algorithm is that no knowledge of the noise distribution is required, and the relative contribution of the LMS, the LMF and the smoothing functionals is adjusted based on the partially restored image.",

keywords = "Kurtosis, Mixed-norms, Regularized image restoration, Smoothing functional",

author = "Hong, {Min Cheol} and Tania Stathaki and Katsaggelos, {Aggelos K.}",

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T1 - An iterative regularized mixed-norm image restoration algorithm

AU - Hong, Min Cheol

AU - Stathaki, Tania

AU - Katsaggelos, Aggelos K.

PY - 1998

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N2 - This paper introduces a regularized mixed-norm image restoration algorithm. A functional which combines the least mean squares (LMS), the least mean fourth (LMF), and a smoothing functional is proposed. A function of the kurtosis is used to determine the relative importance between the LMS and the LMF functionals, and a function of the previous two functionals and the smoothing functionals is utilized for determining the regularization parameter. The two parameters are chosen in such a way that the proposed functional is convex, so that a local minimizer becomes a global minimizer. The novelty of the proposed algorithm is that no knowledge of the noise distribution is required, and the relative contribution of the LMS, the LMF and the smoothing functionals is adjusted based on the partially restored image.

AB - This paper introduces a regularized mixed-norm image restoration algorithm. A functional which combines the least mean squares (LMS), the least mean fourth (LMF), and a smoothing functional is proposed. A function of the kurtosis is used to determine the relative importance between the LMS and the LMF functionals, and a function of the previous two functionals and the smoothing functionals is utilized for determining the regularization parameter. The two parameters are chosen in such a way that the proposed functional is convex, so that a local minimizer becomes a global minimizer. The novelty of the proposed algorithm is that no knowledge of the noise distribution is required, and the relative contribution of the LMS, the LMF and the smoothing functionals is adjusted based on the partially restored image.

KW - Kurtosis

KW - Mixed-norms

KW - Regularized image restoration

KW - Smoothing functional

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ER -

An iterative regularized mixed-norm image restoration algorithm

Abstract

Keywords

ASJC Scopus subject areas

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