A new class of nonlinear hyperbolic-parabolic model for image denoising with forward-backward diffusivity

Abstract

Image denoising and edge detection are two major problems in the area of image processing. Therefore, this study aims to proposes and mathematically analyze a nonlinear diffusion-based hyperbolic-parabolic model for image denoising and edge detection. The proposed model consists of the second derivative concerning time, preserve sharper images, and converges very fast to reduce the noise of the noisy images. The present model is well-posed, and admit a unique weak solution under certain conditions. The results of the model are computed by a finite difference method based on an iterative explicit scheme. Further, the results of the proposed model are compared with the old model for synthetic and real degradations using explicit schemes with forward-backward diffusivity.