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An adaptive algorithm for TV-based model of three norms L-q(q=1/2, 1, 2) in image restoration
Chang, Qianshun1,2; Che, Zengyan1
2018-07-15
Source PublicationAPPLIED MATHEMATICS AND COMPUTATION
ISSN0096-3003
Volume329Pages:251-265
AbstractIn this paper, we present an adaptive method for the TV-based model of three norms L-q(q = 1 2, 1, 2) for the image restoration problem. The algorithm with the L-2 norm is used in the smooth regions, where the value of vertical bar del u vertical bar is small. The algorithm with the L-1/2 norm is applied for the jumps, where the value of vertical bar del u vertical bar is large. When the value of vertical bar del u vertical bar is moderate, the algorithm with the L-1 norm is employed. Thus, the three algorithms are applied for different regions of a given image such that the advantages of each algorithm are adopted. The numerical experiments demonstrate that our adaptive algorithm can not only keep the original edge and original detailed information but also weaken the staircase phenomenon in the restored images. Specifically, in contrast to the L-1 norm as in the Rudin-Osher-Fatemi model, the L-2 norm yields better results in the smooth and flat regions, and the L-1/2 norm is more suitable in regions with strong discontinuities. Therefore, our adaptive algorithm is efficient and robust even for images with large noises. (C) 2018 Elsevier Inc. All rights reserved.
KeywordImage restoration Split Bregman method Alternating minimization method L-1/2 norm L-2 norm
DOI10.1016/j.amc.2018.01.040
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000427813700021
PublisherELSEVIER SCIENCE INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29928
Collection中国科学院数学与系统科学研究院
Affiliation1.Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Chang, Qianshun,Che, Zengyan. An adaptive algorithm for TV-based model of three norms L-q(q=1/2, 1, 2) in image restoration[J]. APPLIED MATHEMATICS AND COMPUTATION,2018,329:251-265.
APA Chang, Qianshun,&Che, Zengyan.(2018).An adaptive algorithm for TV-based model of three norms L-q(q=1/2, 1, 2) in image restoration.APPLIED MATHEMATICS AND COMPUTATION,329,251-265.
MLA Chang, Qianshun,et al."An adaptive algorithm for TV-based model of three norms L-q(q=1/2, 1, 2) in image restoration".APPLIED MATHEMATICS AND COMPUTATION 329(2018):251-265.
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