An Improved Fourth-order PDE for Noise Removal with Dissipation Reduction

Abstract

In this paper we present a method that can reduce the dissipation during fourth-order PDE diffusion processing which is used for noise removal without blocky effect. PDE-based method has been a successful tool for image restoration. But most of PDE methods have a common problem that is the processed image looks like cartoon image. In order to overcome the blocky effect introduced by second order PDE, Yuli You proposed a fourth order PDE method which seeks to minimize a function proportional to the absolute value of the Laplacian operator of the image. But we found that this method can also introduce dissipation during the diffusion process. In order to reduce the dissipation effect, we consider revising the diffusion coefficient. And what we think is to introduce the gradient operator into the diffusion coefficient. This method can reduce the dissipation effect during the denoising process. From the experiment we can see that the dissipation is reduced.