Efficient image denoising technique using the meshless method: Investigation of operator splitting RBF collocation method for two anisotropic diffusion-based PDEs

Abstract

Images taken and stored digitally are often degraded by noise, so that the perceived image quality is significantly decreased in the presence of noise and human gaze behavior is affected by this noise as well. In recent years, image denoising has been modeled as partial differential equations (PDEs), which can be said to eliminate noise as well as preserve image detail is one of their main advantages. Numerical simulation of these PDEs, which are often nonlinear, high-order and high-dimensional, is one of the most challenging topics in this field. In this paper, one of the most powerful meshless numerical approaches, the operator splitting radial basis function (RBF) collocation method, is introduced to solve two modified versions of the Perona-Malik (PM) equation. The method splits each problem into several equations each of which is solved in one direction so as to make the major problem solvable in a smaller size. Furthermore, being in one direction makes it possible to solve the equations without any need for domain decomposition and its complexities. An unconditionally stable method (Crank-Nicolson) is used for discretizing time in this paper. Using meshless approaches in the image processing problems makes sense since the structure of digital images consist of pixels that corresponds to the distributed nodes of the meshless method so the complex time consuming domain construction of the finite element methods is avoided to get higher speeds in obtaining the desired denoised results. Some images with different noise levels are denoised using the presented method in the section of numerical results to show the desirable performance of the method. Also, the quality of the denoised images are concluded in tables which can be used to compare the obtained results.