A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting
In this research, we study the convex minimization problem in the form of the sum of two proper, lower-semicontinuous, and convex functions. We introduce a new projected forward-backward algorithm using linesearch and inertial techniques. We then establish a weak convergence theorem under mild condi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/8/890 |
| _version_ | 1797537401918193664 |
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| author | Suthep Suantai Kunrada Kankam Prasit Cholamjiak |
| author_facet | Suthep Suantai Kunrada Kankam Prasit Cholamjiak |
| author_sort | Suthep Suantai |
| collection | DOAJ |
| description | In this research, we study the convex minimization problem in the form of the sum of two proper, lower-semicontinuous, and convex functions. We introduce a new projected forward-backward algorithm using linesearch and inertial techniques. We then establish a weak convergence theorem under mild conditions. It is known that image processing such as inpainting problems can be modeled as the constrained minimization problem of the sum of convex functions. In this connection, we aim to apply the suggested method for solving image inpainting. We also give some comparisons to other methods in the literature. It is shown that the proposed algorithm outperforms others in terms of iterations. Finally, we give an analysis on parameters that are assumed in our hypothesis. |
| first_indexed | 2024-03-10T12:14:41Z |
| format | Article |
| id | doaj.art-a6c39aa50208468f8a6fcf3276c42457 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T12:14:41Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a6c39aa50208468f8a6fcf3276c424572023-11-21T15:56:05ZengMDPI AGMathematics2227-73902021-04-019889010.3390/math9080890A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image InpaintingSuthep Suantai0Kunrada Kankam1Prasit Cholamjiak2Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandSchool of Science, University of Phayao, Phayao 56000, ThailandSchool of Science, University of Phayao, Phayao 56000, ThailandIn this research, we study the convex minimization problem in the form of the sum of two proper, lower-semicontinuous, and convex functions. We introduce a new projected forward-backward algorithm using linesearch and inertial techniques. We then establish a weak convergence theorem under mild conditions. It is known that image processing such as inpainting problems can be modeled as the constrained minimization problem of the sum of convex functions. In this connection, we aim to apply the suggested method for solving image inpainting. We also give some comparisons to other methods in the literature. It is shown that the proposed algorithm outperforms others in terms of iterations. Finally, we give an analysis on parameters that are assumed in our hypothesis.https://www.mdpi.com/2227-7390/9/8/890convex minimizationimage inpaintinginertial techniquesweak convergence |
| spellingShingle | Suthep Suantai Kunrada Kankam Prasit Cholamjiak A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting Mathematics convex minimization image inpainting inertial techniques weak convergence |
| title | A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting |
| title_full | A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting |
| title_fullStr | A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting |
| title_full_unstemmed | A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting |
| title_short | A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting |
| title_sort | projected forward backward algorithm for constrained minimization with applications to image inpainting |
| topic | convex minimization image inpainting inertial techniques weak convergence |
| url | https://www.mdpi.com/2227-7390/9/8/890 |
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