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

Existence of an exact relationship between the maximum likehood method (MLM) and autoregressive (AR) signal modeling in multi-dimensional (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 non-uniformly or uniformly.