A fast algorithm for linear estimation of three-dimensional homogeneous anisotropic random fields

This paper presents an algorithm for estimating a three-dimensional homogeneous random field from noisy observations inside a sphere of finite radius. It thus constitutes an alternative to solving a multi-dimensional Wiener-Hopf equation. The algorithm is fast in that it exploits the structure of the integral equation kernel to reduce the computation required to construct the optimal filter. It is thus an extension of similar fast algorithms that have been obtained for the one-dimensional and isotropic random field estimation problems. The problem of estimating an isotropic field at the center of a sphere of observations is treated as a special case.