Cramer-Rao Bounds for Parametric Estimation of Target Boundaries 
in Nonlinear Inverse Scattering Problems

by Jong  Chul Ye, Yoram Bresler and Pierre Moulin

 
We present new methods for computing fundamental performance limits for parametric
shape estimation in inverse scattering problems, such as passive radar imaging.
We evaluate Cram\'{e}r-Rao lower bounds (CRB) on shape estimation accuracy
using the domain derivative technique from nonlinear inverse scattering theory.
The CRB provides an unbeatable performance limit for any unbiased estimator, 
and under fairly mild regularity conditions, is asymptotically
achieved by the maximum likelihood estimator (MLE), hence
serving as a predictor of the high signal-to-noise ratio performance of the MLE.
Furthermore, the resultant CRB's are used to define a global confidence region,
centered around the true boundary, in which the boundary estimate lies with
a prescribed probability.  These global confidence regions conveniently display
the uncertainty in various geometric parameters such as shape, size, orientation,
and position of the estimated target, and facilitate geometric inferences.
Numerical simulations are performed using the layer approach and the Nystr\"{o}m
method for computation of domain derivatives, and using Fourier descriptors for
target shape parameterization.  This analysis demonstrates the accuracy and
generality of the proposed methods.