@article{7af36144eee04ff4a0a34b16691aa8d0,
title = "Fixed-point algorithms for a TVL1 image restoration model",
abstract = "In this paper, we study fixed point proximity algorithms for a TVL1 restoration model recovering blurred images with impulsive noise, and image inpainting. The model that minimizes the sum of a data fidelity term in the l1 -norm, a term in l2 -norm and total-variation regularization term is strictly convex. We obtain the solution of the model through finding a fixed point of a nonlinear mapping expressed in terms of the proximity operator of the l1-norm or the l2-norm, each of which is explicitly given. The non-expansivity of the mapping is also analysed theoretically. This formulation naturally leads to fixed-point algorithms for numerical treatment of the model. Numerical experiments demonstrate that the proposed algorithms perform favourably.",
keywords = "35A15, 49J40, 68U10, 94A08, Total variation, deblurring, impulsive noise, inpainting, proximity operator",
author = "Jian Lu and Ke Qiao and Lixin Shen and Yuru Zou",
note = "Funding Information: This work was supported in part by the US National Science Foundation # DMS-1522332, by the National Natural Science Foundation of China #61373087, #11201312, #61272252, #61472257, by the China Scholarship Council, by the Foundation for Distinguished Young Teachers in Guangdong, China #Yq2013144, by the Guangdong Natural Science Foundation of China #2015A030313557, #2015A030313550, by the HD Video R & D Platform for Intelligent Analysis and Processing in Guangdong Engineering Technology Research Centre of Colleges and Universities #GCZX-A1409, and by the Shenzhen Key Laboratory of Media Security. The authors would like to thank the anonymous referees for their careful reading, helpful comments, and suggestions that led to a significant improvement of the manuscript. Funding Information: This work was supported in part by the US National Science Foundation # DMS-1522332, by the National Natural Science Foundation of China #61373087, #11201312, #61272252, #61472257, by the China Scholarship Council, by the Foundation for Distinguished Young Teachers in Guangdong, China #Yq2013144, by the Guangdong Natural Science Foundation of China #2015A030313557, #2015A030313550, by the HD Video R & D Platform for Intelligent Analysis and Processing in Guangdong Engineering Technology Research Centre of Colleges and Universities #GCZX-A1409, and by the Shenzhen Key Laboratory of Media Security .",
year = "2018",
month = sep,
day = "2",
doi = "10.1080/00207160.2017.1343470",
language = "English (US)",
volume = "95",
pages = "1829--1844",
journal = "International Journal of Computer Mathematics",
issn = "0020-7160",
publisher = "Taylor and Francis Ltd.",
number = "9",
}