| Autor: |
Shahbaz Ahmad, Faisal Fairag, Adel M. Al-Mahdi, Jamshaid ul Rahman |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
AIMS Mathematics, Vol 7, Iss 10, Pp 17989-18009 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2022991?viewType=HTML |
| Popis: |
Image deblurring models with a mean curvature functional has been widely used to preserve edges and remove the staircase effect in the resulting images. However, the Euler-Lagrange equations of a mean curvature model can be used to solve fourth-order non-linear integro-differential equations. Furthermore, the discretization of fourth-order non-linear integro-differential equations produces an ill-conditioned system so that the numerical schemes like Krylov subspace methods (conjugate gradient etc.) have slow convergence. In this paper, we propose an augmented Lagrangian method for a mean curvature-based primal form of the image deblurring problem. A new circulant preconditioned matrix is introduced to overcome the problem of slow convergence when employing a conjugate gradient method inside of the augmented Lagrangian method. By using the proposed new preconditioner fast convergence has been observed in the numerical results. Moreover, a comparison with the existing numerical methods further reveal the effectiveness of the preconditioned augmented Lagrangian method. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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