Compound PDE-Based Additive Denoising Solution Combining an Improved Anisotropic Diffusion Model to a 2D Gaussian Filter Kernel

Abstract

A second-order nonlinear anisotropic diffusion-based model for Gaussian additive noise removal is proposed. The method is based on a properly constructed edge-stopping function and provides an efficient detail-preserving denoising. It removes additive noise, overcomes blurring effect, reduces the image staircasing and does not generate multiplicative noise, thus preserving boundaries and all the essential image features very well. The corresponding PDE model is solved by a robust finite-difference based iterative scheme consistent with the diffusion model. The method converges very fast to the model solution, the existence and regularity of which is rigorously proved.