A fourth order partial differential equation model from the Weber´s total variation for image restoration

Here we examine the partial regularity of minimums of a Laplace functional with the Weber TV image restoration in Bounded Variation space. Most conventional image processors consider little the influence of human vision psychology. This paper proposed a new functional. Furthermore, this functional is not only to use Laplace operator but also to add the human psychology system. Of course, because we add the influence of human vision psychology for the regularity item, this adds the difficult extent of the proposed problem of this text. Due to the singular nature of the Laplace, we study a regularized Laplace. With the proof of the experiment, it was to be found that this functional thus smoothes the image, and preserves edges via total variation because this functional lead into a higher order equation-a fourth order partial differential equation.