Open AccessTwo new preconditioners for mean curvature-based image deblurring problem
Author(s) -
Shahbaz Ahmad,
Adel M. AlMahdi,
Rashad Ahmed
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021802
Subject(s) - deblurring , krylov subspace , mathematics , discretization , convergence (economics) , algorithm , curvature , nonlinear system , mean curvature , image (mathematics) , image restoration , iterative method , mathematical analysis , computer science , image processing , geometry , artificial intelligence , economics , physics , quantum mechanics , economic growth
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.