Noise removal algorithm by using total variation norm and its euler-lagrange equation

Abstract

The Total Variation norm (TV-norm) for removing noise preserves edges well but has the unexpected effect which transforms smooth regions into piecewise constant regions. In this paper, we propose the model which includes the second order differential term to TV-norm that reduces the staircase effect, while preserving sharp jump discontinuous edges. Also this has influence on convergence to the smaller iterations than only TV-norm model. For the convergence of the iteration, the algorithm depends on the choice of these parameters. The optimal values of the parameter $α_1$ is proportional to the amount of noise variance, and the parameter $α_2$ is concerned with the speed of convergence. We solve the denoising problem using the Euler-Lagrange equation and the Newton method.