An efficient maximum entropy technique for 2-D isotropic random fields

A linear MEM (maximum-entropy spectral estimation method) algorithm for 2-D isotropic random fields is introduced. Unlike general 2-D covariances, isotropic covariance functions that are positive definite on a disk are known to be extendible. A computationally efficient procedure is developed for computing the MEM isotropic covariance function that is given over a finite disk of radius 2R . It is shown that the isotropic MEM problem has a linear solution and that it is equivalent to the problem of constructing the optimal linear filter for estimating the underlying isotropic field at a point on the boundary of a disk radius R, given noisy measurements of the field inside the disk. The procedure is guaranteed to yield a valid isotropic spectral estimate and is computationally efficient since it requires only O(BRL²) operations, where L is the number of points used to discretize the interval [0, R] and B is the bandwidth in the wave-number plane of the spectrum that to be estimated. Examples are presented to illustrate the behaviour of the algorithm and its high-resolution property