Pre-conditioning CQ algorithm for solving the split feasibility problem and its application to image restoration problem
Pre-conditioning CQ algorithm for solving the split feasibility problem and its application to image restoration problem
In this study, we define two pre-conditioning CQ algorithms for the split feasibility problem by using self-adaptive and line-search techniques in the real Hilbert space. One of the self-adaptive techniques is used to obtain optimal step size. These techniques do not require prior knowledge of the operator norm or estimation of the matrix norm. We also establish weak convergence theorems with respect to particular norms. As an application, numerical experiments show that the proposed algorithm is effective in image restoration problem.
Split feasibility problem, image restoration problem, line search technique, pre-conditioning CQ algorithm, self-adaptive technique
Altıparmak, Ebru
dd55ed8d-7678-42a9-a449-9db6a8837167
Jolaoso, Lateef Olakunle
102467df-eae0-4692-8668-7f73e8e02546
Karahan, Ibrahim
b434e27f-591a-4806-930a-c37c82b7ef74
Rehman, Habib ur
25006c6a-ac68-424c-9764-2da7cafa152d
Altıparmak, Ebru
dd55ed8d-7678-42a9-a449-9db6a8837167
Jolaoso, Lateef Olakunle
102467df-eae0-4692-8668-7f73e8e02546
Karahan, Ibrahim
b434e27f-591a-4806-930a-c37c82b7ef74
Rehman, Habib ur
25006c6a-ac68-424c-9764-2da7cafa152d
Altıparmak, Ebru, Jolaoso, Lateef Olakunle, Karahan, Ibrahim and Rehman, Habib ur
(2024)
Pre-conditioning CQ algorithm for solving the split feasibility problem and its application to image restoration problem.
Optimization.
(doi:10.1080/02331934.2024.2358412).
Abstract
In this study, we define two pre-conditioning CQ algorithms for the split feasibility problem by using self-adaptive and line-search techniques in the real Hilbert space. One of the self-adaptive techniques is used to obtain optimal step size. These techniques do not require prior knowledge of the operator norm or estimation of the matrix norm. We also establish weak convergence theorems with respect to particular norms. As an application, numerical experiments show that the proposed algorithm is effective in image restoration problem.
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More information
Accepted/In Press date: 7 May 2024
e-pub ahead of print date: 30 May 2024
Keywords:
Split feasibility problem, image restoration problem, line search technique, pre-conditioning CQ algorithm, self-adaptive technique
Identifiers
Local EPrints ID: 492804
URI: http://eprints.soton.ac.uk/id/eprint/492804
ISSN: 0233-1934
PURE UUID: d0415b63-9aa3-4bfa-93fb-43bb99969e38
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Date deposited: 14 Aug 2024 16:53
Last modified: 15 Aug 2024 02:17
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Author:
Ebru Altıparmak
Author:
Ibrahim Karahan
Author:
Habib ur Rehman
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