An Anisotropic Fourth-Order Partial Differential Equation for Noise Removal

Abstract

Fourth-order nonlinear diffusion filters are isotropic filters in which the strength of diffusion at regions with strong image features such as regions with an edge or texture is reduced leading to their preservation. However, the optimal choice of parameter in the numerical solver of these filters for having a minimal distortion of the image features results in a very slow convergence rate and formation of speckle noise on the denoised image especially when the noise level is moderately high. In this paper, a new fourth-order nonlinear diffusion filter is introduced, which have an anisotropic behavior on the image features. In the proposed filter, it is shown that a suitable design of a set of diffusivity functions to unevenly control the diffusion on the directions of level set and gradient leads to a fast convergent filter with a good edge preservation capability. The comparison of the results obtained by the proposed filter with that of the classical and recently developed techniques shows that the proposed method produces a noticeable improvement in the quality of denoised images evaluated subjectively and quantitatively as well as a substantial increment of the convergence rate comparing to the classical filter.