Existence and Uniqueness of Weak Solutions for a New Class of Convex Optimization Problems Related to Image Analysis
This paper proposes a new anisotropic diffusion model in image restoration that is understood from a variational optimization of an energy functional. Initially, a family of new diffusion functions based on cubic Hermite spline is provided for optimal image denoising. After that, the existence and u...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6691795 |
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| author | Anas Tiarimti Alaoui Mostafa Jourhmane |
| author_facet | Anas Tiarimti Alaoui Mostafa Jourhmane |
| author_sort | Anas Tiarimti Alaoui |
| collection | DOAJ |
| description | This paper proposes a new anisotropic diffusion model in image restoration that is understood from a variational optimization of an energy functional. Initially, a family of new diffusion functions based on cubic Hermite spline is provided for optimal image denoising. After that, the existence and uniqueness of weak solutions for the corresponding Euler–Lagrange equation are proven in an appropriate functional space, and a consistent and stable numerical model is also shown. We complement this work by illustrating some experiments on different actual brain Magnetic Resonance Imaging (MRI) scans, showing the proposed model’s impressive results. |
| format | Article |
| id | doaj-art-3329afaa4f554d6982297e01997b8499 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3329afaa4f554d6982297e01997b84992025-02-03T01:25:25ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66917956691795Existence and Uniqueness of Weak Solutions for a New Class of Convex Optimization Problems Related to Image AnalysisAnas Tiarimti Alaoui0Mostafa Jourhmane1TIAD Laboratory, Department of Mathematics, Faculty of Sciences and Technics, Sultan Moulay Slimane University, Beni Mellal, MoroccoTIAD Laboratory, Department of Mathematics, Faculty of Sciences and Technics, Sultan Moulay Slimane University, Beni Mellal, MoroccoThis paper proposes a new anisotropic diffusion model in image restoration that is understood from a variational optimization of an energy functional. Initially, a family of new diffusion functions based on cubic Hermite spline is provided for optimal image denoising. After that, the existence and uniqueness of weak solutions for the corresponding Euler–Lagrange equation are proven in an appropriate functional space, and a consistent and stable numerical model is also shown. We complement this work by illustrating some experiments on different actual brain Magnetic Resonance Imaging (MRI) scans, showing the proposed model’s impressive results.http://dx.doi.org/10.1155/2021/6691795 |
| spellingShingle | Anas Tiarimti Alaoui Mostafa Jourhmane Existence and Uniqueness of Weak Solutions for a New Class of Convex Optimization Problems Related to Image Analysis Journal of Mathematics |
| title | Existence and Uniqueness of Weak Solutions for a New Class of Convex Optimization Problems Related to Image Analysis |
| title_full | Existence and Uniqueness of Weak Solutions for a New Class of Convex Optimization Problems Related to Image Analysis |
| title_fullStr | Existence and Uniqueness of Weak Solutions for a New Class of Convex Optimization Problems Related to Image Analysis |
| title_full_unstemmed | Existence and Uniqueness of Weak Solutions for a New Class of Convex Optimization Problems Related to Image Analysis |
| title_short | Existence and Uniqueness of Weak Solutions for a New Class of Convex Optimization Problems Related to Image Analysis |
| title_sort | existence and uniqueness of weak solutions for a new class of convex optimization problems related to image analysis |
| url | http://dx.doi.org/10.1155/2021/6691795 |
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