Bayesian Estimation of a Random Field with Discontinuities

Abstract

This paper deals with the estimation problem of a random field with discontinuities. The method is based on the Bayesian approach. When the Bayesian method is applied to the estimation problem of a random field, a prior information about the random field plays a crucial role. It is revealed that in the case of the random field with discontinuities, as the prior information, the Cauchy probability distribution for the spatial variation of the random field is superior to the Gaussian probability distribution which is widely used. Then, it is shown that the estimation algorithm obtained is realized in a parallel manner using a neural network model.