Relationship between likelihood method and autoregressive modeling in multidimensional power spectrum estimation

Existence of an exact relationship between the maximum likelihood method (MLM) and autoregressive (AR) signal modeling in multidimensional (m-D) power spectral estimation is shown. For one-dimensional (1-D), uniformly sampled autocorrelation functions (ACF), Burg has shown a relationship between the maximum entropy method (MEM) and MLM spectral estimates. In this note we show a similar relationship between the MLM and AR spectral estimates for m-D (or 1-D) signals sampled nonuniformly or uniformly.