Journal article
alpha l(1) - beta l(2) regularization for sparse recovery
Inverse problems, Vol.35(12), 125009
12/01/2019
DOI: 10.1088/1361-6420/ab34b5
Abstract
This paper presents a novel regularization with a non-convex, non-smooth term of the form with parameters to solve ill-posed linear problems with sparse solutions. We investigate the existence, stability and convergence of the regularized solution. It is shown that this type of regularization is well-posed and yields sparse solutions. Under an appropriate source condition, we get the convergence rate in the -norm for a priori and a posteriori parameter choice rules, respectively. A numerical algorithm is proposed and analyzed based on an iterative threshold strategy with the generalized conditional gradient method. We prove the convergence even though the regularization term is non-smooth and non-convex. The algorithm can easily be implemented because of its simple structure. Some numerical experiments are performed to test the efficiency of the proposed approach. The experiments show that regularization with performs better in comparison with the classical sparsity regularization and can be used as an alternative to the regularizer.
Details
- Title: Subtitle
- alpha l(1) - beta l(2) regularization for sparse recovery
- Creators
- Liang Ding - Northeast Forestry UniversityWeimin Han - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Inverse problems, Vol.35(12), 125009
- Publisher
- IOP PUBLISHING LTD
- DOI
- 10.1088/1361-6420/ab34b5
- ISSN
- 0266-5611
- eISSN
- 1361-6420
- Number of pages
- 26
- Grant note
- 201806605017 / China Scholarship Council LBH-Q16008 / Heilongjiang Postdoctoral Research Developmental Fund 41304093 / National Natural Science Foundation of China
- Language
- English
- Date published
- 12/01/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984241055302771
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