An innovative inertial extra-proximal gradient algorithm for solving convex optimization problems with application to image and signal processing
This study introduces an innovative approach to address convex optimization problems, with a specific focus on applications in image and signal processing. The research aims to develop a self-adaptive extra proximal algorithm that incorporates an inertial term to effectively tackle challenges in con...
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| Vydáno v: | Heliyon Ročník 9; číslo 10; s. e20513 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Ltd
01.10.2023
Elsevier |
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| ISSN: | 2405-8440, 2405-8440 |
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| Abstract | This study introduces an innovative approach to address convex optimization problems, with a specific focus on applications in image and signal processing. The research aims to develop a self-adaptive extra proximal algorithm that incorporates an inertial term to effectively tackle challenges in convex optimization. The study's significance lies in its contribution to advancing optimization techniques in the realm of image deblurring and signal reconstruction. The proposed methodology involves creating a novel self-adaptive extra proximal algorithm, analyzing its convergence rigorously to ensure reliability and effectiveness. Numerical examples, including image deblurring and signal reconstruction tasks using only 10% of the original signal, illustrate the practical applicability and advantages of the algorithm. By introducing an inertial term within the extra proximal framework, the algorithm demonstrates potential for faster convergence and improved optimization outcomes, addressing real-world challenges of image enhancement and signal reconstruction. The algorithm's incorporation of an inertial term showcases its potential for faster convergence and improved optimization outcomes. This research significantly contributes to the field of optimization techniques, particularly in the context of image and signal processing applications. |
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| AbstractList | This study introduces an innovative approach to address convex optimization problems, with a specific focus on applications in image and signal processing. The research aims to develop a self-adaptive extra proximal algorithm that incorporates an inertial term to effectively tackle challenges in convex optimization. The study's significance lies in its contribution to advancing optimization techniques in the realm of image deblurring and signal reconstruction. The proposed methodology involves creating a novel self-adaptive extra proximal algorithm, analyzing its convergence rigorously to ensure reliability and effectiveness. Numerical examples, including image deblurring and signal reconstruction tasks using only 10% of the original signal, illustrate the practical applicability and advantages of the algorithm. By introducing an inertial term within the extra proximal framework, the algorithm demonstrates potential for faster convergence and improved optimization outcomes, addressing real-world challenges of image enhancement and signal reconstruction. The algorithm's incorporation of an inertial term showcases its potential for faster convergence and improved optimization outcomes. This research significantly contributes to the field of optimization techniques, particularly in the context of image and signal processing applications. This study introduces an innovative approach to address convex optimization problems, with a specific focus on applications in image and signal processing. The research aims to develop a self-adaptive extra proximal algorithm that incorporates an inertial term to effectively tackle challenges in convex optimization. The study's significance lies in its contribution to advancing optimization techniques in the realm of image deblurring and signal reconstruction. The proposed methodology involves creating a novel self-adaptive extra proximal algorithm, analyzing its convergence rigorously to ensure reliability and effectiveness. Numerical examples, including image deblurring and signal reconstruction tasks using only 10% of the original signal, illustrate the practical applicability and advantages of the algorithm. By introducing an inertial term within the extra proximal framework, the algorithm demonstrates potential for faster convergence and improved optimization outcomes, addressing real-world challenges of image enhancement and signal reconstruction. The algorithm's incorporation of an inertial term showcases its potential for faster convergence and improved optimization outcomes. This research significantly contributes to the field of optimization techniques, particularly in the context of image and signal processing applications.This study introduces an innovative approach to address convex optimization problems, with a specific focus on applications in image and signal processing. The research aims to develop a self-adaptive extra proximal algorithm that incorporates an inertial term to effectively tackle challenges in convex optimization. The study's significance lies in its contribution to advancing optimization techniques in the realm of image deblurring and signal reconstruction. The proposed methodology involves creating a novel self-adaptive extra proximal algorithm, analyzing its convergence rigorously to ensure reliability and effectiveness. Numerical examples, including image deblurring and signal reconstruction tasks using only 10% of the original signal, illustrate the practical applicability and advantages of the algorithm. By introducing an inertial term within the extra proximal framework, the algorithm demonstrates potential for faster convergence and improved optimization outcomes, addressing real-world challenges of image enhancement and signal reconstruction. The algorithm's incorporation of an inertial term showcases its potential for faster convergence and improved optimization outcomes. This research significantly contributes to the field of optimization techniques, particularly in the context of image and signal processing applications. |
| ArticleNumber | e20513 |
| Author | Akewe, Hudson Memon, M. Asif Seidu, Jamel Olilima, Joshua Mogbademu, Adesanmi Obalalu, Adebowale Martins |
| Author_xml | – sequence: 1 givenname: Joshua orcidid: 0000-0002-5914-3351 surname: Olilima fullname: Olilima, Joshua organization: Department of Mathematical Sciences, Augustine University, Ilara-Epe, Lagos, Nigeria – sequence: 2 givenname: Adesanmi surname: Mogbademu fullname: Mogbademu, Adesanmi organization: Department of Mathematics, University of Lagos, Akoka, Lagos, Nigeria – sequence: 3 givenname: M. Asif surname: Memon fullname: Memon, M. Asif organization: Department of Mathematics and Social Sciences, Sukkur IBA University, Sukkur, 65200, Sindh, Pakistan – sequence: 4 givenname: Adebowale Martins surname: Obalalu fullname: Obalalu, Adebowale Martins organization: Department of Mathematical Sciences, Augustine University, Ilara-Epe, Lagos, Nigeria – sequence: 5 givenname: Hudson surname: Akewe fullname: Akewe, Hudson organization: Department of Mathematics, University of Lagos, Akoka, Lagos, Nigeria – sequence: 6 givenname: Jamel orcidid: 0000-0003-4729-765X surname: Seidu fullname: Seidu, Jamel email: jseidu@umat.edu.gh organization: School of Railways and Infrastructure Development, University of Mines and Technology (UMaT) Essikado, Sekondi-Takoradi, Ghana |
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| Cites_doi | 10.1080/17455030.2022.2152907 10.1287/moor.19.4.790 10.1007/s11784-018-0526-5 10.1137/080716542 10.1142/S0217979223500650 10.1007/s00500-021-05596-6 10.1002/cmm4.1088 10.1007/s10288-020-00440-3 10.1080/10556788.2016.1214959 10.1007/s40314-018-0684-5 10.1186/s13634-023-01005-2 10.1137/S0363012998338806 10.1007/978-1-4419-9569-8_10 10.3934/math.2022453 10.1007/s10107-019-01415-x 10.3390/math10193573 10.1023/A:1011253113155 10.1186/s13660-015-0857-3 10.24033/bsmf.1625 10.1016/j.apnum.2022.01.016 10.1007/s10092-018-0292-1 10.4208/nmtma.2018.s05 10.1186/s13660-020-02522-6 10.1080/00036811.2020.1736287 10.3934/math.20221126 |
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| Keywords | Signal & image processing Weak convergence Inertial method Convex minimization problem Forward-backward algorithm |
| Language | English |
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| SubjectTerms | algorithms Convex minimization problem domain fields Forward-backward algorithm image analysis Inertial method Signal & image processing system optimization Weak convergence |
| Title | An innovative inertial extra-proximal gradient algorithm for solving convex optimization problems with application to image and signal processing |
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