ON TWO-DIMENSIONAL MARKOV SPECTRAL ESTIMATION.

We developed methods for two-dimensional (2-D) spectral estimation from raw data using Markov random field (MRF) models. We assume that the given finite data are represented by an appropriate Gaussian MRF model. This assumption reduces the spectral estimation problem to that of estimating the appropriate structure and the parameters of the MRF model. Parameter estimation is computationally tractable when specific boundary conditions are assumed. The toroidal lattice representation used in this paper yields computationally manageable algorithms for maximum likelihood (ML) estimation of parameters. By using the fact that the 2-D maximum entropy spectral (MES) estimate has a structure similar to the MRF power spectrum and a sample correlation matching property we argue that for infinite number of observations the MRF spectrum derived is the conventionally understood 2-D MES estimate.