Yuying Shi

A new deblurring and denoising algorithm is proposed, for isotropic total variation-based image restoration. The algorithm consists of an efficient solver for the nonlinear system and an acceleration strategy for the outer iteration. For the nonlinear system, the split Bregman method is used to convert it into linear system, and an algebraic multigrid method is applied to solve the linearized system. For the outer iteration, we have conducted formal convergence analysis to determine an auxiliary linear term that significantly stabilizes and accelerates the outer iteration. Numerical experiments demonstrate that our algorithm for deblurring and denoising problems is efficient.

In this paper we present a simple but very effective pretreatment on the initial value applied to two kinds of time dependent image restoration model. Two kinds of images and two kinds of boundary conditions (BCs) are used for our numerical experiments. Numerical results demonstrate that the little change accelerates the convergence and gets a better restoration effect.

In this paper, the Crank-Nicholson semi-implicit difference scheme is applied to discrete the Rudin-Osher-Fatemi model which was proposed by Rudin et al. in 1992. The semi-implicit discrete scheme avoids the shortcomings of instability and many iterative numbers that the explicit discrete scheme has. We propose an image denoising algorithm in the matrix form. The experimental results show that the new matrix semi-explicit scheme is efficient.