Gaussian processes of nonlinear diffusion filtering

Nonlinear diffusion filtering can be improved if viewed as Bayesian Gaussian process regression. We relate the covariance functions of the diffusion process outcome to the spatial diffusion operator and show how Bayesian evidence criterion can he utilized to determine the parameters of the nonlinear diffusivity and the optimal diffusion stopping time. Computational example is given where the nonlinear diffusion filtering outperforms typical Gaussian process regression.