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Volume 8
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Article

A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method

by
Adisak Hanjing
1 and
Suthep Suantai
2,*
1
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2
Data Science Research Center, Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 378; https://doi.org/10.3390/math8030378
Submission received: 19 February 2020 / Revised: 5 March 2020 / Accepted: 6 March 2020 / Published: 8 March 2020
(This article belongs to the Special Issue Mathematical Approaches to Image Processing with Applications)
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Abstract

In this paper, a new accelerated fixed point algorithm for solving a common fixed point of a family of nonexpansive operators is introduced and studied, and then a weak convergence result and the convergence behavior of the proposed method is proven and discussed. Using our main result, we obtain a new accelerated image restoration algorithm, called the forward-backward modified W-algorithm (FBMWA), for solving a minimization problem in the form of the sum of two proper lower semi-continuous and convex functions. As applications, we apply the FBMWA algorithm to solving image restoration problems. We analyze and compare convergence behavior of our method with the others for deblurring the image. We found that our algorithm has a higher efficiency than the others in the literature.
Keywords: Hilbert space; proximal methods; fixed point algorithm; forward-backward algorithm; image restoration problem Hilbert space; proximal methods; fixed point algorithm; forward-backward algorithm; image restoration problem

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MDPI and ACS Style

Hanjing, A.; Suantai, S. A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method. Mathematics 2020, 8, 378. https://doi.org/10.3390/math8030378

AMA Style

Hanjing A, Suantai S. A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method. Mathematics. 2020; 8(3):378. https://doi.org/10.3390/math8030378

Chicago/Turabian Style

Hanjing, Adisak, and Suthep Suantai. 2020. "A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method" Mathematics 8, no. 3: 378. https://doi.org/10.3390/math8030378

APA Style

Hanjing, A., & Suantai, S. (2020). A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method. Mathematics, 8(3), 378. https://doi.org/10.3390/math8030378

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