A Method of Sieves for Multiresolution Spectrum Estimation and Radar Imaging

A method of sieves using splines is proposed for regularizing maximum-likelihood estimates of power spectra. This method has several important properties, including the flexibility to be used at multiple resolution levels. The resolution level is defined in terms of the support of the polynomial B-splines used. Using a discrepancy measure derived from the Kullback-Leibler divergence of parameterized density functions, an expression for the optimal rate of growth of the sieve is derived. While the sieves may be defined on nonuniform grids, in the case of uniform grids the optimal sieve size corresponds to an optimal resolution. Iterative algorithms for obtaining the maximum-likelihood sieve estimates are derived. Applications to spectrum estimation and radar imaging are proposed.