Multidimensional maximum-entropy covariance extension

A universal characterization of multi-dimensional maximum-entropy covariances is presented. We show that the maximum-entropy extension of an arbitrary covariance band of a (nonstationary) multi-dimensional signal must have a banded inverse. Furthermore, we show that for one-dimensional signals such banded-inverse covariances are characterized by finite-order autoregressive models. The same kind of model is inadequate for multi-dimensional signals, but it can be used to approximate maximum-entropy covariances.