A Partial Regularity Result for the Combined Total Variation Functional for Image Restoration

Most conventional image processors consider little the influence of human vision psychology. Here we examine the partial regularity of minimums of a combined functional with the Weber TV image restoration in Bounded Variation space. This paper proposed a new functional. Furthermore, this functional is also a combination of a regularized p-Laplace for the part of the image with small gradient and a total variation functional for the part with large gradient. Of course, we all add the influence of human vision psychology for the regularity item. Due to the singular nature of the p-Laplace, we study a regularized p-Laplace. This functional thus smoothes the image where the gradient is small and preserves edges via total variation where the gradient is large.