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A NONLOCAL LOW-RANK REGULARIZATION METHOD FOR FRACTAL IMAGE CODING

Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China

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HUAXUAN HU

Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China

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JIAN LU

Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China

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XIAOXIA LIU

https://orcid.org/0000-0002-2289-7520

Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China

E-mail Address: xliu@szu.edu.cn

Corresponding author.

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QINGTANG JIANG

Department of Mathematics and Statistics, University of Missouri-St. Louis, St. Louis, MO 63121, USA

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, and

GUOHUI SONG

Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA

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https://doi.org/10.1142/S0218348X21501255Cited by:8 (Source: Crossref)

Abstract

Fractal coding has been widely used as an image compression technique in many image processing problems in the past few decades. On the other hand side, most of the natural images have the characteristic of nonlocal self-similarity that motivates low-rank representations of them. We would employ both the fractal image coding and the nonlocal self-similarity priors to achieve image compression in image denoising problems. Specifically, we propose a new image denoising model consisting of three terms: a patch-based nonlocal low-rank prior, a data-fidelity term describing the closeness of the underlying image to the given noisy image, and a quadratic term measuring the closeness of the underlying image to a fractal image. Numerical results demonstrate the superior performance of the proposed model in terms of peak-signal-to-noise ratio, structural similarity index and mean absolute error.

Keywords:

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