Iterative thresholding algorithm based on non-convex method for modified lp-norm regularization minimization

Recently, the lp-norm regularization minimization problem (Ppλ) has attracted great attention in compressed sensing. However, the lp-norm ‖x‖pp in problem (Ppλ) is nonconvex and non-Lipschitz for all p∈(0,1), and there are not many optimization theories and methods proposed to solve this problem. In...

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Published inJournal of computational and applied mathematics Vol. 347; pp. 173 - 180
Main Authors Cui, Angang, Peng, Jigen, Li, Haiyang, Wen, Meng, Jia, Junxiong
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2019
Subjects
[formula omitted] algorithm
[formula omitted]-norm
Compressed sensing
Modified [formula omitted]-norm
49M20
lp-norm
65K10
1∕2−ϵ algorithm
90C26
Compressed sensing
Modified lp-norm
Online AccessGet full text
ISSN0377-0427
1879-1778
DOI10.1016/j.cam.2018.08.021

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Abstract Recently, the lp-norm regularization minimization problem (Ppλ) has attracted great attention in compressed sensing. However, the lp-norm ‖x‖pp in problem (Ppλ) is nonconvex and non-Lipschitz for all p∈(0,1), and there are not many optimization theories and methods proposed to solve this problem. In fact, it is NP-hard for all p∈(0,1) andλ>0. In this paper, we study one modified lp-norm regularization minimization problem to approximate the NP-hard problem (Ppλ). Inspired by the good performance of Half algorithm in some sparse signal recovery problems, an iterative thresholding algorithm is proposed to solve our modified lp-norm regularization minimization problem (Pp,1∕2,ϵλ). Numerical results on some sparse signal recovery problems show that our algorithm performs effectively in finding the sparse signals compared with some state-of-art methods.
AbstractList Recently, the lp-norm regularization minimization problem (Ppλ) has attracted great attention in compressed sensing. However, the lp-norm ‖x‖pp in problem (Ppλ) is nonconvex and non-Lipschitz for all p∈(0,1), and there are not many optimization theories and methods proposed to solve this problem. In fact, it is NP-hard for all p∈(0,1) andλ>0. In this paper, we study one modified lp-norm regularization minimization problem to approximate the NP-hard problem (Ppλ). Inspired by the good performance of Half algorithm in some sparse signal recovery problems, an iterative thresholding algorithm is proposed to solve our modified lp-norm regularization minimization problem (Pp,1∕2,ϵλ). Numerical results on some sparse signal recovery problems show that our algorithm performs effectively in finding the sparse signals compared with some state-of-art methods.
Author Jia, Junxiong
Cui, Angang
Li, Haiyang
Peng, Jigen
Wen, Meng
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Keywords 49M20
lp-norm
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1∕2−ϵ algorithm
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Compressed sensing
Modified lp-norm
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SubjectTerms [formula omitted] algorithm
[formula omitted]-norm
Compressed sensing
Modified [formula omitted]-norm
Title Iterative thresholding algorithm based on non-convex method for modified lp-norm regularization minimization
URI https://dx.doi.org/10.1016/j.cam.2018.08.021
Volume 347
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