Circulant preconditioners for mean curvature-based image deblurring problem

Abstract

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.