(A) numerical method in image processing

Abstract

This paper is concerned with a reconstruction of contaminated images with noise. Our approach is based on a damped Newton method. In this paper, we propose the model, Euler-Lagrange Equation, which includes the second order differential term to TV-norm that reduces the undesirable blocky (or staircase) effect([16]), while preserving sharp jump discontinuous edges. One of the difficulties in solving the Euler-Lagrange equation is the presence of a nonlinear and non-differentiability term, which causes convergence difficulties for Newton``s method even when combined with a globalization technique such as a line search. The idea of our new algorithm is to remove some of the singularity caused by the non-differentiability of the objective function, $\frac{▽_u}{│▽_u │}$, before we apply a linearization technique such as Damped Newton Method.