Journal article
A projected gradient method for alpha l(1)-beta l(2) sparsity regularization
Inverse problems, Vol.36(12), 125012
12/01/2020
DOI: 10.1088/1361-6420/abc857
Abstract
The non-convex alpha||.||l(1)-beta||.||l(2)(alpha >=beta >= 0) regularization is a new approach for sparse recovery. A minimizer of the alpha||.||(l)1-beta||.||l(2) regularized function can be computed by applying the ST-(alpha l(1) - beta l(2)) algorithm which is similar to the classical iterative soft thresholding algorithm (ISTA). It is known that ISTA converges quite slowly, and a faster alternative to ISTA is the projected gradient (PG) method. However, the conventional PG method is limited to solve problems with the classical l(1) sparsity regularization. In this paper, we present two accelerated alternatives to the ST-(alpha l(1) - beta l(2)) algorithm by extending the PG method to the non-convex alpha||.||l(1)-beta||.||l(2) sparsity regularization. Moreover, we discuss a strategy to determine the radius R of the l(1)-ball constraint by Morozov's discrepancy principle. Numerical results are reported to illustrate the efficiency of the proposed approach.
Details
- Title: Subtitle
- A projected gradient method for alpha l(1)-beta l(2) sparsity regularization
- Creators
- Liang Ding - Northeast Forestry UniversityWeimin Han - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Inverse problems, Vol.36(12), 125012
- DOI
- 10.1088/1361-6420/abc857
- ISSN
- 0266-5611
- eISSN
- 1361-6420
- Publisher
- IOP PUBLISHING LTD
- Number of pages
- 30
- Grant note
- 2572018BC02 / Fundamental Research Funds for the Central Universities LBH-Q16008 / Heilongjiang Postdoctoral Research Developmental Fund 41304093 / National Nature Science Foundation of China
- Language
- English
- Date published
- 12/01/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984240878702771
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