Surface characterization using frequency diverse scattering measurements and regularity models

Accurate classification and characterization of image regions is often an important goal for the users of coherent imaging systems such as synthetic aperture radar (SAR). Many surfaces measured by remote sensing systems can be stochastically described by a regularity model. This parametric point-process model describes a 1-D surface in terms of the mean and variance of the interscatterer distances. Variations of these parameters can describe scatterer distributions ranging from totally random to nearly periodic. Under certain conditions, a closed-form approximation to the mean power spectrum of finite-length data intervals exists. The estimation of model parameters from measured spectra can then be cast as an optimization problem in which the total squared error between the approximation and the simple periodogram is minimized. We examine the general performance limitations of such an optimization procedure, determining how approximation error, signal-to-noise ratio, and frequency-sampling rate affect the feasibility and accuracy of parameter estimation. We determine under what conditions the approximation may be used. We find that parameter estimation is feasible at a frequency-sampling rate that is well below that suggested by the power spectral density (PSD). This suggests that it is possible to obtain parameter estimates by comparing sparse narrow-band frequency measurements to the PSD of the point-process and thereby obtain information about the surface on subresolution scales