Image denoising algorithm with a three-dimensional grid system of coupled nonlinear elements

This paper presents an image denoising algorithm with a three-dimensional grid system of coupled nonlinear elements. The system consists of a two-dimensional image grid and a one-dimensional grid representing a quantized image brightness. At each grid point, a FitzHugh-Nagumo type nonlinear element is placed and coupled with other elements placed at its nearest neighboring grid points. The FitzHugh-Nagumo element is described with a set of time-evolving ordinary differential equations, and is tuned to be excitable. When we externally stimulate the grid system with an image brightness distribution, we could observe that noise in the distribution was reduced and signal was strengthened as time proceeds. Thus, the image denoising algorithm utilizes this property of the grid system, in which we propose to modify external stimuli so as to have broad Gaussian distributions. We confirm performance of the algorithm on artificial and real images in comparison with two classical algorithms of a diffusion equation and median filtering.