An Extended Reweighted ℓ1 Minimization Algorithm for Image Restoration

This paper proposes an effective extended reweighted ℓ1 minimization algorithm (ERMA) to solve the basis pursuit problem minu∈Rn{||u||1:Au=f} in compressed sensing, where A∈Rm×n, m≪n. The fast algorithm is based on linearized Bregman iteration with soft thresholding operator and generalized inverse...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 9; no. 24; p. 3224
Main Authors: Huang, Sining, Chen, Yupeng, Qiao, Tiantian
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.12.2021
Subjects:
Algorithms
Food science
Generalized inverse
Image restoration
Iterative methods
Linear programming
Optimization
Signal to noise ratio
Sparsity
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:This paper proposes an effective extended reweighted ℓ1 minimization algorithm (ERMA) to solve the basis pursuit problem minu∈Rn{||u||1:Au=f} in compressed sensing, where A∈Rm×n, m≪n. The fast algorithm is based on linearized Bregman iteration with soft thresholding operator and generalized inverse iteration. At the same time, it also combines the iterative reweighted strategy that is used to solve minu∈Rn{||u||pp:Au=f} problem, with the weight ωi(u,p)=(ε+|ui|2)p/2−1. Numerical experiments show that this ℓ1 minimization persistently performs better than other methods. Especially when p=0, the restored signal by the algorithm has the highest signal to noise ratio. Additionally, this approach has no effect on workload or calculation time when matrix A is ill-conditioned.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math9243224