Morozov's discrepancy principle for <inline-formula><tex-math id="M1">$ \alpha\ell_1-\beta\ell_2 $</tex-math></inline-formula> sparsity regularization

Liang Ding; Weimin Han

doi:10.3934/ipi.2022035

$Morozov's discrepancy principle for <inline-formula><tex-math id="M1">$ \alpha\ell_1-\beta\ell_2 $</tex-math></inline-formula> sparsity regularization$

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Morozov's discrepancy principle for $ \alpha\ell_1-\beta\ell_2 $ sparsity regularization

Liang Ding and Weimin Han

Inverse problems and imaging (Springfield, Mo.), Vol.17(1), pp.157-179

2023

DOI: 10.3934/ipi.2022035

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Abstract

In this paper, Morozov’s discrepancy principle is considered for the non-convex αℓ1 − βℓ2 sparsity regularization (α > β > 0). It is shown that if τ > 1 satisfies some conditions, there exists a regularization parameter α such that δ ≤ ∥A(xδα,β)− yδ ∥Y ≤ τδ holds. Furthermore, it is shown that α converges to 0 as δ → 0. In addition, well-posedness and convergence rate results are presented for the regularized solution under Morozov’s discrepancy principle. Numerical simulation results are reported to illustrate the efficiency of the proposed approach.

Details

Title: Subtitle: Morozov's discrepancy principle for $ \alpha\ell_1-\beta\ell_2 $ sparsity regularization
Creators: Liang Ding
Weimin Han
Resource Type: Journal article
Publication Details: Inverse problems and imaging (Springfield, Mo.), Vol.17(1), pp.157-179
DOI: 10.3934/ipi.2022035
ISSN: 1930-8337
eISSN: 1930-8345
Language: English
Date published: 2023
Academic Unit: Mathematics
Record Identifier: 9984353647702771

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