A fast alternating minimization algorithm for total variation deblurring without boundary artifacts

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	A fast alternating minimization algorithm for total variation deblurring without boundary artifacts
	Bai, Zheng-Jian ; Cassani, Daniele ; Donatelli, Marco ; Serra-Capizzano, Stefano ; Bai ZJ(白正简)
刊名	http://dx.doi.org/10.1016/j.jmaa.2014.01.061
	2014-07-01
关键词	CONSTRAINED OPTIMIZATION IMAGE DECONVOLUTION PRECONDITIONERS MODELS
英文摘要	National Natural Science Foundation of China [11271308]; NCET; Internationalization Grant of U. Insubria; MIUR [20083KLJEZ]; Recently, a fast alternating minimization algorithm for total variation image deblurring (FTVd) has been presented by Wang, Yang, Yin, and Zhang (2008) [32]. The method in a nutshell consists of a discrete Fourier transform-based alternating minimization algorithm with periodic boundary conditions and in which two fast Fourier transforms (FFTs) are required per iteration. In this paper, we propose an alternating minimization algorithm for the continuous version of the total variation image deblurring problem. We establish convergence of the proposed continuous alternating minimization algorithm. The continuous setting is very useful to have a unifying representation of the algorithm, independently of the discrete approximation of the deconvolution problem, in particular concerning the strategies for dealing with boundary artifacts. Indeed, an accurate restoration of blurred and noisy images requires a proper treatment of the boundary. A discrete version of our continuous alternating minimization algorithm is obtained following two different strategies: the imposition of appropriate boundary conditions and the enlargement of the domain. The first one is computationally useful in the case of a symmetric blur, while the second one can be efficiently applied for a nonsymmetric blur. Numerical tests show that our algorithm generates higher quality images in comparable running times with respect to the Fast Total Variation deconvolution algorithm. (C) 2014 Elsevier Inc. All rights reserved.
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91327]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Bai, Zheng-Jian,Cassani, Daniele,Donatelli, Marco,et al. A fast alternating minimization algorithm for total variation deblurring without boundary artifacts[J]. http://dx.doi.org/10.1016/j.jmaa.2014.01.061,2014.
APA	Bai, Zheng-Jian,Cassani, Daniele,Donatelli, Marco,Serra-Capizzano, Stefano,&白正简.(2014).A fast alternating minimization algorithm for total variation deblurring without boundary artifacts.http://dx.doi.org/10.1016/j.jmaa.2014.01.061.
MLA	Bai, Zheng-Jian,et al."A fast alternating minimization algorithm for total variation deblurring without boundary artifacts".http://dx.doi.org/10.1016/j.jmaa.2014.01.061 (2014).