An overview of iterative methods based on orthogonal projections
This paper investigates the linear feasibility problem (LFP), which plays a fundamental role in image reconstruction, especially in applications such as computed tomography and signal processing. The goal is to find a point in the intersection of a finite collection of convex sets defined by linear...
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| Format: | Article |
| Language: | English |
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Qom University of Technology
2025-06-01
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| Series: | Mathematics and Computational Sciences |
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| Online Access: | https://mcs.qut.ac.ir/article_725395_ab949adf96b69d099ef027c047c65212.pdf |
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| author | Touraj Nikazad Mona Khakzad |
| author_facet | Touraj Nikazad Mona Khakzad |
| author_sort | Touraj Nikazad |
| collection | DOAJ |
| description | This paper investigates the linear feasibility problem (LFP), which plays a fundamental role in image reconstruction, especially in applications such as computed tomography and signal processing. The goal is to find a point in the intersection of a finite collection of convex sets defined by linear constraints. We provide a structured overview and comparison of existing orthogonal projection-based iterative methods for solving LFPs, including sequential, simultaneous, and block-iterative algorithms. While these methods have been studied individually in the literature, our work highlights their theoretical underpinnings, practical performance, and convergence properties in a unified framework. We also revisit and refine known convergence theorems, discussing their assumptions and implications in the context of real-world reconstruction problems. The novelty of this study lies in its comprehensive synthesis of algorithmic strategies along with a critical analysis of their relative strengths, limitations, and applicability. This work aims to clarify the landscape of projection methods for LFPs and to guide the selection or development of more effective reconstruction techniques in practice. |
| format | Article |
| id | doaj-art-1f8ec4b744f9468d82c39d019d4e4a4c |
| institution | Kabale University |
| issn | 2717-2708 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Qom University of Technology |
| record_format | Article |
| series | Mathematics and Computational Sciences |
| spelling | doaj-art-1f8ec4b744f9468d82c39d019d4e4a4c2025-08-20T03:28:04ZengQom University of TechnologyMathematics and Computational Sciences2717-27082025-06-016211212410.30511/mcs.2025.2050369.1288725395An overview of iterative methods based on orthogonal projectionsTouraj Nikazad0Mona Khakzad1Applied Mathematics Department, School of Mathematics and computer Sciences, Iran University of Science and Technology, Tehran, Iran.Applied Mathematics Department, School of Mathematics and computer Sciences, Iran University of Science and Technology, Tehran, Iran.This paper investigates the linear feasibility problem (LFP), which plays a fundamental role in image reconstruction, especially in applications such as computed tomography and signal processing. The goal is to find a point in the intersection of a finite collection of convex sets defined by linear constraints. We provide a structured overview and comparison of existing orthogonal projection-based iterative methods for solving LFPs, including sequential, simultaneous, and block-iterative algorithms. While these methods have been studied individually in the literature, our work highlights their theoretical underpinnings, practical performance, and convergence properties in a unified framework. We also revisit and refine known convergence theorems, discussing their assumptions and implications in the context of real-world reconstruction problems. The novelty of this study lies in its comprehensive synthesis of algorithmic strategies along with a critical analysis of their relative strengths, limitations, and applicability. This work aims to clarify the landscape of projection methods for LFPs and to guide the selection or development of more effective reconstruction techniques in practice.https://mcs.qut.ac.ir/article_725395_ab949adf96b69d099ef027c047c65212.pdfconvex feasibility problemprojectionsiterative methods |
| spellingShingle | Touraj Nikazad Mona Khakzad An overview of iterative methods based on orthogonal projections Mathematics and Computational Sciences convex feasibility problem projections iterative methods |
| title | An overview of iterative methods based on orthogonal projections |
| title_full | An overview of iterative methods based on orthogonal projections |
| title_fullStr | An overview of iterative methods based on orthogonal projections |
| title_full_unstemmed | An overview of iterative methods based on orthogonal projections |
| title_short | An overview of iterative methods based on orthogonal projections |
| title_sort | overview of iterative methods based on orthogonal projections |
| topic | convex feasibility problem projections iterative methods |
| url | https://mcs.qut.ac.ir/article_725395_ab949adf96b69d099ef027c047c65212.pdf |
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