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

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...

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Vydané v:	Mathematics (Basel) Ročník 8; číslo 3; s. 378
Hlavní autori:	Hanjing, Adisak, Suantai, Suthep
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	MDPI AG 01.03.2020
Predmet:	fixed point algorithm forward-backward algorithm hilbert space image restoration problem proximal methods
ISSN:	2227-7390, 2227-7390
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Popis
Shrnutí:	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.
ISSN:	2227-7390 2227-7390
DOI:	10.3390/math8030378