An analog neural net performing multidimensional maximum entropy spectral estimation

A general algorithm is presented for computationally efficient multidimensional maximum entropy (ME) spectral estimation. The estimator is equivalent to an analog neural net that is governed by an energy function that measures the degree of constraint satisfaction, i.e., correlation-matching property. The multidimensional ME (MDME) spectral-estimation problem is defined. ME spectral estimation is formulated as an initial-value problem. The MDME spectral estimators, or algorithms, for solving the initial-value problem are developed. The neural net algorithm is derived, and simulated experiments with 1-D or 2-D signals are conducted. In each, the assumed true spectrum is given and autocorrelations at a number of horizontally and vertically equally spaced lags are calculated from the Fourier transform of the true spectrum. The overall results indicate very good performance in estimating ME spectra, even in cases where there are few autocorrelation measurements.