Two new 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 produce a nonlinear ill-conditioned system which affect the convergence of the numerical algorithms like Krylov subspa...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 12; pp. 13824 - 13844
Main Authors Ahmad, Shahbaz, Al-Mahdi, Adel M., Ahmed, Rashad
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
ill-posed problem
image deblurring
mean curvature
numerical analysis
preconditioning
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021802

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Summary: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 produce a nonlinear ill-conditioned system which affect the convergence of the numerical algorithms like Krylov subspace methods. To overcome this difficulty, in this paper, we present two new symmetric positive definite (SPD) preconditioners. An efficient algorithm is presented for the mean curvature-based image deblurring problem which combines a fixed point iteration (FPI) 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 preconditioners.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021802