Stochastic Partial Differential Equations as priors in ensemble methods for solving inverse problems

Abstract

This article describes a coordinate free approach to modelling stochastic textures through the application of stochastic partial differential equations. The intended application is that of sampling from a prior probability density in the solution of inverse problems by Bayesian filtering methods. In simpler cases analytical formulae for the correlation functions can be derived. Such formulae can then be used to guide parameter selection in the general case where numerical methods are necessary.