The use of physics-informed neural network approach to image restoration via nonlinear PDE tools

Abstract

In this work, we propose a physics-informed solution for a blending PDE model with application in image denoising and edge-preserving. The blending model contains isotropic diffusion (ID) model and the modified Perona-Malik model introduced by Catte et al. Then we solve this model applying a physics-informed approach. Solving the new blending model is done using DeepXDE, which is a deep learning library for solving differential equations, by considering the image as input. Error analysis for neural network approximations of the new PDE model is shown. Applying PSNR criteria for some images, it can be seen that the proposed method can compete with solving denoising PDE models using finite difference method (FDM).