A key task in Inverse Synthetic Aperture Radar (ISAR) imaging and many other applications is estimating the power spectrum of a two-dimensional random process from data measurements. Often the data sampling points do not correspond to a uniformly-spaced rectangular lattice. A particular method is reported herein for performing spectrum analysis from data measured on an irregular lattice. The method employs certain optimal weights, termed Generalized Prolate Spheroidal Sequences, that are determined from a generalized matrix eigenvec luor problem. Because the computational burden of the eigenvector solution can be impractical for large sampling lattices, computationally efficient sub-optimal approximations to the optimal eigenvector weights are proposed. These approximate weights result from careful modification of both the optimization criterion and the subspace over which the criterion is optimized. Near-optimal results can be obtained with a significant reduction in computation. A numerical example is presented for a particular ISAR application to verify the utility of the approximations.