Assessment of the Negentropy Based Stopping Time Criterion in the Diffusive Restoration of Digital Images

Abstract

One method successfully employed to denoise digital images is the diffusive iterative filtering. An important point of this technique is the estimation of the stopping time of the diffusion process. In this paper, we propose a stopping time criterion based on the evolution of the negentropy of the 'noise signal' with the diffusion parameter. The nonlinear diffusive filter implemented with this stopping criterion is evaluated by using several noisy test images with different statistics. Assuming that images are corrupted by additive Gaussian noise, a statistical measure of the Gaussianity can be used to estimate the amount of noise removed from noisy images. In particular, the differential entropy function or, equivalently, the negentropy are robust measures of the Gaussianity. Because of computational complexity of the negentropy function, it is estimated by using an approximation of the negentropy introduced by Hyvarinen in the context of independent component analysis.