NONLOCAL LOW RANK REGULARIZATION METHOD FOR FRACTAL IMAGE CODING UNDER SALT-AND-PEPPER NOISE

Huan Pan, Zhengyu Liang, Jian Lu, Kai Tu and Ning Xie
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Huan Pan: Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China†National Center for Applied Mathematics Shenzhen (NCAMS), Shenzhen 518055, P. R. China‡The Pazhou Lab, Guangzhou 510335, P. R. China
Zhengyu Liang: Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China†National Center for Applied Mathematics Shenzhen (NCAMS), Shenzhen 518055, P. R. China‡The Pazhou Lab, Guangzhou 510335, P. R. China
Jian Lu: Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China†National Center for Applied Mathematics Shenzhen (NCAMS), Shenzhen 518055, P. R. China‡The Pazhou Lab, Guangzhou 510335, P. R. China
Kai Tu: �College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China
Ning Xie: �Guangdong Key Laboratory of Intelligent Information Processing, College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 07, 1-16

Abstract: Image denoising has been a fundamental problem in the field of image processing. In this paper, we tackle removing impulse noise by combining the fractal image coding and the nonlocal self-similarity priors to recover image. The model undergoes a two-stage process. In the first phase, the identification and labeling of pixels likely to be corrupted by salt-and-pepper noise are carried out. In the second phase, image denoising is performed by solving a constrained convex optimization problem that involves an objective functional composed of three terms: a data fidelity term to measure the similarity between the underlying and observed images, a regularization term to represent the low-rank property of a matrix formed by nonlocal patches of the underlying image, and a quadratic term to measure the closeness of the underlying image to a fractal image. To solve the resulting problem, a combination of proximity algorithms and the weighted singular value thresholding operator is utilized. The numerical results demonstrate an improvement in the structural similarity (SSIM) index and peak signal-to-noise ratio.

Keywords: Image Denoising; Fractal Coding; Low-Rank Regularization; Salt-and-Pepper Noise (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500767

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