Variational Methods for Coherence Enhancing Image Denoising

Abstract

Image denoising by regularization of coherence enhancing functionals have become increasingly standard due to their structural preservation properties. One example of coherence enhancing regularization is formulated by Weickert (1999) as a PDE. A typical drawback of such methods, however, is the creation of artifacts structures created from random noise by the denoiser. In this paper, we use coherence enhancing regularization approaches to create and test low-level denoising algorithms based on the regularization method of Weickert. To combat the artifact generation of the method, we propose as an alternative a non-local functional, with the goal of inheriting the anisotropical enhancement properties of the Weickert functional, while at the same time suppressing artifact generation. Mathematically, the paper compares the two coherence enhancing functionals and covers in detail both theory on existence of minimizers and how to find these minima. Concluding the paper, we present some numerical results demonstrating the denoising properties of both the Weickert functional and the proposed non-local functional.