The extension of Pisarenko's method to multiple dimensions

Pisarenko's method of spectral estimation, which models the spectrum as a sum of impulses plus a white noise component, was originally formulated for the time series case. The extension of this method to multiple dimensions and non-uniformly spaced correlation samples involves several fascinating problems. Pisarenko's estimate, which in the time series case involves the solution of an eigenvalue problem, is shown more generally to involve the solution of a linear optimization problem. The computation of Pisarenko's estimate by the application of the simplex method to the linear programming problem is considered. The possibility of a faster multiple exchange algorithm is discussed.