  Delayed target response in synthetic aperture radar (SAR) imaging can be
obscured by the range-delay ambiguity and speckle. To analyze the range-delay
ambiguity, one extends the standard SAR formulation and allows both the target
reflectivity and the image to depend not only on the coordinates, but also on
the response delay. However, this still leaves the speckle unaccounted for. Yet
speckle is commonly found in SAR images of extended targets, and a statistical
approach is usually employed to describe it. We have developed a simple model
of a delayed scatterer by modifying the random function that describes a
homogeneous extended scatterer. Our model allows us to obtain a relation
between the deterministic parameters of the target model and statistical
moments of the SAR image. We assume a regular shape of the antenna trajectory,
and our model targets are localized in at least one space-time coordinate; this
permits analytical formulation for statistical moments of the image. The
problem of reconstruction of coordinate-delay reflectivity function is reduced
to that of discrimination between instantaneous and delayed scatterers; for the
latter problem, the maximum likelihood based image processing procedure has
been developed. We perform Monte-Carlo simulation and evaluate performance of
the classification procedure for a simple dependence of scatterer reflectivity
on the delay time.
