Multidimensional MEM spectral estimation

The problem of multidimensional maximum entropy method (MEM) spectral estimation from nonuniformly spaced correlation measurements is investigated. A necessary and sufficient condition is derived for the existence and uniqueness of the MEM spectral estimate in its usual form. It is shown that this condition is not satisfied in many multidimensional problems of interest, although it is satisfied in the important practical case of spectral supports composed of a finite number of points. When the existence condition is satisfied, calculation of the MEM estimate reduces to the solution of a finite-dimensional convex optimization problem. The application of standard optimization techniques to this problem results in iterative computational algorithms which are guaranteed to converge. The algorithms so obtained are compared to those previously proposed and a spectral estimation example is presented.