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Volume 42, Issue 3
Sparse Recovery Based on the Generalized Error Function

Zhiyong Zhou

DOI: 10.4208/jcm.2204-m2021-0288

J. Comp. Math., 42 (2024), pp. 679-704.

Published online: 2024-04

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  • Abstract

In this paper, we offer a new sparse recovery strategy based on the generalized error function. The introduced penalty function involves both the shape and the scale parameters, making it extremely flexible. For both constrained and unconstrained models, the theoretical analysis results in terms of the null space property, the spherical section property and the restricted invertibility factor are established. The practical algorithms via both the iteratively reweighted $ℓ_1$ and the difference of convex functions algorithms are presented. Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances. Its practical application in magnetic resonance imaging (MRI) reconstruction is also investigated.

  • Keywords

Sparse recovery, Generalized error function, Nonconvex regularization, Iterative reweighted L1, Difference of convex functions algorithms.

  • AMS Subject Headings

94A12, 94A20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-679, author = {Zhou , Zhiyong}, title = {Sparse Recovery Based on the Generalized Error Function}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {3}, pages = {679--704}, abstract = {

In this paper, we offer a new sparse recovery strategy based on the generalized error function. The introduced penalty function involves both the shape and the scale parameters, making it extremely flexible. For both constrained and unconstrained models, the theoretical analysis results in terms of the null space property, the spherical section property and the restricted invertibility factor are established. The practical algorithms via both the iteratively reweighted $ℓ_1$ and the difference of convex functions algorithms are presented. Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances. Its practical application in magnetic resonance imaging (MRI) reconstruction is also investigated.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2204-m2021-0288}, url = {http://global-sci.org/intro/article_detail/jcm/23032.html} }
TY - JOUR T1 - Sparse Recovery Based on the Generalized Error Function AU - Zhou , Zhiyong JO - Journal of Computational Mathematics VL - 3 SP - 679 EP - 704 PY - 2024 DA - 2024/04 SN - 42 DO - http://doi.org/10.4208/jcm.2204-m2021-0288 UR - https://global-sci.org/intro/article_detail/jcm/23032.html KW - Sparse recovery, Generalized error function, Nonconvex regularization, Iterative reweighted L1, Difference of convex functions algorithms. AB -

In this paper, we offer a new sparse recovery strategy based on the generalized error function. The introduced penalty function involves both the shape and the scale parameters, making it extremely flexible. For both constrained and unconstrained models, the theoretical analysis results in terms of the null space property, the spherical section property and the restricted invertibility factor are established. The practical algorithms via both the iteratively reweighted $ℓ_1$ and the difference of convex functions algorithms are presented. Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances. Its practical application in magnetic resonance imaging (MRI) reconstruction is also investigated.

Zhiyong Zhou. (2024). Sparse Recovery Based on the Generalized Error Function. Journal of Computational Mathematics. 42 (3). 679-704. doi:10.4208/jcm.2204-m2021-0288
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