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A projected gradient method for alpha l(1)-beta l(2) sparsity regularization
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A projected gradient method for alpha l(1)-beta l(2) sparsity regularization

Liang Ding and Weimin Han
Inverse problems, Vol.36(12), 125012
12/01/2020
DOI: 10.1088/1361-6420/abc857
url
https://arxiv.org/pdf/2007.15263View
Open Access

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.
Mathematics Physical Sciences Physics Mathematics, Applied Physics, Mathematical Science & Technology

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