Circulant preconditioners for mean curvature-based image deblurring problem

The mean curvature-based image deblurring model is widely used to enhance the quality of the deblurred images. However, the discretization of the associated Euler–Lagrange equations produces a nonlinear ill-conditioned system which affects the convergence of the numerical algorithms such as Krylov s...

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Autores principales:	Shahbaz Ahmad, Faisal Fairag
Formato:	article
Lenguaje:	EN
Publicado:	SAGE Publishing 2021
Materias:	Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/642d1acaa0224a70b20e9250c47a4433
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spelling	oai:doaj.org-article:642d1acaa0224a70b20e9250c47a44332021-11-21T02:03:47ZCirculant preconditioners for mean curvature-based image deblurring problem1748-302610.1177/17483026211055679https://doaj.org/article/642d1acaa0224a70b20e9250c47a44332021-11-01T00:00:00Zhttps://doi.org/10.1177/17483026211055679https://doaj.org/toc/1748-3026The mean curvature-based image deblurring model is widely used to enhance the quality of the deblurred images. However, the discretization of the associated Euler–Lagrange equations produces a nonlinear ill-conditioned system which affects the convergence of the numerical algorithms such as Krylov subspace methods (generalized minimal residual etc.) To overcome this difficulty, in this paper, we present three new circulant preconditioners. An efficient algorithm is presented for the mean curvature-based image deblurring problem, which combines a fixed point iteration with new preconditioned matrices to handle the nonlinearity and ill-conditioned nature of the large system. The eigenvalues analysis is also presented in the paper. Fast convergence has shown in the numerical results by using the proposed new circulant preconditioners.Shahbaz AhmadFaisal FairagSAGE PublishingarticleApplied mathematics. Quantitative methodsT57-57.97MathematicsQA1-939ENJournal of Algorithms & Computational Technology, Vol 15 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939
spellingShingle	Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939 Shahbaz Ahmad Faisal Fairag Circulant preconditioners for mean curvature-based image deblurring problem
description	The mean curvature-based image deblurring model is widely used to enhance the quality of the deblurred images. However, the discretization of the associated Euler–Lagrange equations produces a nonlinear ill-conditioned system which affects the convergence of the numerical algorithms such as Krylov subspace methods (generalized minimal residual etc.) To overcome this difficulty, in this paper, we present three new circulant preconditioners. An efficient algorithm is presented for the mean curvature-based image deblurring problem, which combines a fixed point iteration with new preconditioned matrices to handle the nonlinearity and ill-conditioned nature of the large system. The eigenvalues analysis is also presented in the paper. Fast convergence has shown in the numerical results by using the proposed new circulant preconditioners.
format	article
author	Shahbaz Ahmad Faisal Fairag
author_facet	Shahbaz Ahmad Faisal Fairag
author_sort	Shahbaz Ahmad
title	Circulant preconditioners for mean curvature-based image deblurring problem
title_short	Circulant preconditioners for mean curvature-based image deblurring problem
title_full	Circulant preconditioners for mean curvature-based image deblurring problem
title_fullStr	Circulant preconditioners for mean curvature-based image deblurring problem
title_full_unstemmed	Circulant preconditioners for mean curvature-based image deblurring problem
title_sort	circulant preconditioners for mean curvature-based image deblurring problem
publisher	SAGE Publishing
publishDate	2021
url	https://doaj.org/article/642d1acaa0224a70b20e9250c47a4433
work_keys_str_mv	AT shahbazahmad circulantpreconditionersformeancurvaturebasedimagedeblurringproblem AT faisalfairag circulantpreconditionersformeancurvaturebasedimagedeblurringproblem
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Circulant preconditioners for mean curvature-based image deblurring problem

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