Double inertial parameters forward-backward splitting method: applications to compressed sensing, image processing, and SCAD penalty problems
Double inertial parameters forward-backward splitting method: applications to compressed sensing, image processing, and SCAD penalty problems
In this paper, a forward-backward splitting algorithm with two inertial parameters (one non-negative and the other non-positive) extrapolation step is proposed for finding a zero point of the sum of maximal monotone and co-coercive operators in real Hilbert spaces. One of the interesting features of our proposed algorithm is that no online rule on the inertial parameters with the iterates is needed. The weak convergence result of the proposed algorithm is established under some standard assumptions. Numerical results arising from LASSO problems in compressed sensing, image processing, and SCAD penalty problems are provided to illustrate the behavior of our proposed algorithm.
Compressed sensing, Forward-backward splitting, Image processing, Two-step inertial, Weak convergence
627-646
Jolaoso, Lateef Olakunle
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Shehu, Yekini
df727925-5bf0-457a-87fa-f70de3bfd11a
Yao, Jen Chih
036d51bb-3618-4966-a72f-707a4eb6091b
Xu, Renqi
fb90ad57-eb26-4750-90cc-ceef5cf90de7
1 August 2023
Jolaoso, Lateef Olakunle
102467df-eae0-4692-8668-7f73e8e02546
Shehu, Yekini
df727925-5bf0-457a-87fa-f70de3bfd11a
Yao, Jen Chih
036d51bb-3618-4966-a72f-707a4eb6091b
Xu, Renqi
fb90ad57-eb26-4750-90cc-ceef5cf90de7
Jolaoso, Lateef Olakunle, Shehu, Yekini, Yao, Jen Chih and Xu, Renqi
(2023)
Double inertial parameters forward-backward splitting method: applications to compressed sensing, image processing, and SCAD penalty problems.
Journal of Nonlinear and Variational Analysis, 7 (4), .
(doi:10.23952/jnva.7.2023.4.10).
Abstract
In this paper, a forward-backward splitting algorithm with two inertial parameters (one non-negative and the other non-positive) extrapolation step is proposed for finding a zero point of the sum of maximal monotone and co-coercive operators in real Hilbert spaces. One of the interesting features of our proposed algorithm is that no online rule on the inertial parameters with the iterates is needed. The weak convergence result of the proposed algorithm is established under some standard assumptions. Numerical results arising from LASSO problems in compressed sensing, image processing, and SCAD penalty problems are provided to illustrate the behavior of our proposed algorithm.
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JNVA2023-4-10
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Jola-Bilevel-EP-2022
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Accepted/In Press date: 30 March 2023
Published date: 1 August 2023
Additional Information:
Funding Information:
The authors are grateful to the reviewers for useful suggestions which improved the contents of this paper. The third was supported by the Grant MOST 111-2115-M-039-001-MY2.
Keywords:
Compressed sensing, Forward-backward splitting, Image processing, Two-step inertial, Weak convergence
Identifiers
Local EPrints ID: 481246
URI: http://eprints.soton.ac.uk/id/eprint/481246
ISSN: 2560-6921
PURE UUID: 4747e739-37fd-449d-b6d4-5afc48c892dd
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Date deposited: 21 Aug 2023 16:47
Last modified: 18 Mar 2024 04:04
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Contributors
Author:
Yekini Shehu
Author:
Jen Chih Yao
Author:
Renqi Xu
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