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.