A METHOD OF SIEVES FOR MULTIRESOLUTION
SPECTRUM ESTIMATION AND RADAR IMAGING

by Pierre MOULIN, Joseph A. O'SULLIVAN and Donald L. SNYDER

A method of sieves using splines is proposed for regularizing
maximum-likelihood estimates when
a nonnegative function is to be estimated.  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.