An Extended Reweighted ℓ 1 Minimization Algorithm for Image Restoration

Sining Huang, Yupeng Chen and Tiantian Qiao
Additional contact information
Sining Huang: Department of Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China
Yupeng Chen: Department of Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China
Tiantian Qiao: Department of Computational Mathematics, China University of Petroleum (East China), Qingdao 266580, China

Mathematics, 2021, vol. 9, issue 24, 1-15

Abstract: This paper proposes an effective extended reweighted ℓ 1 minimization algorithm (ERMA) to solve the basis pursuit problem min u ∈ R n { | | u | | 1 : A u = f } in compressed sensing, where A ∈ R m × 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 min u ∈ R n { | | u | | p p : A u = f } problem, with the weight ω i ( u , p ) = ( ε + | u i | 2 ) p / 2 − 1 . Numerical experiments show that this ℓ 1 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.

Keywords: extended reweighted ? 1 minimization; fast algorithm; image restoration; iterative generalized inverse (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/24/3224/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/24/3224/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:24:p:3224-:d:701665

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().