Journal article
αl1-βl2 sparsity regularization for nonlinear ill-posed problems
Journal of computational and applied mathematics, Vol.450, 115987
11/01/2024
DOI: 10.1016/j.cam.2024.115987
Abstract
In this paper, the alpha||center dot||l(1)-beta||center dot||l(2) sparsity regularization with parameters alpha >= beta >= 0 is studied for nonlinear ill-posed inverse problems. The well-posedness of the regularization is investigated. Compared to the case where alpha > beta >= 0, the results for the case alpha = beta>0 are weaker due to the lack of coercivity and Radon-Riesz property of the regularization term. Under certain conditions on the nonlinearity of F, sparsity is shown for every minimizer of the alpha||center dot||l(1)-beta||center dot||l(2) regularized inverse problem. Moreover, for the case alpha > beta >= 0, convergence rates O(delta(1)/(2)) and O(delta) are proved for the regularized solution toward a sparse exact solution, under different yet commonly adopted conditions on the nonlinearity of F. The iterative soft thresholding algorithm is shown to be useful to solve the alpha||center dot|l(1)-beta||center dot||l(2) regularized problem for nonlinear ill-posed equations. Numerical results illustrate the efficiency of the proposed method.
Details
- Title: Subtitle
- αl1-βl2 sparsity regularization for nonlinear ill-posed problems
- Creators
- Liang Ding - Northeast Forestry UniversityWeimin Han - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of computational and applied mathematics, Vol.450, 115987
- Publisher
- Elsevier
- DOI
- 10.1016/j.cam.2024.115987
- ISSN
- 0377-0427
- eISSN
- 1879-1778
- Number of pages
- 21
- Language
- English
- Date published
- 11/01/2024
- Academic Unit
- Mathematics
- Record Identifier
- 9984749734102771
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