Techniques for sub-resolution surface characterization using coherent diversity measurements
Abstract
This dissertation examines the feasibility of obtaining small-scale surface information from frequency-diverse measurements of surfaces that are stochastically described by a regularity model. This parametric point-process model describes a one-dimensional surface in terms of the mean and variance of the inter-scatterer distances, and can represent scatterer distributions ranging from totally random to nearly periodic. The problem of estimating model parameters from measured spectra is solved by optimizing the total squared-error between closed-form approximations of the mean power spectra of finite-length data intervals and the simple periodogram. The dissertation examines the general performance limitations of such a procedure, determining how approximation error, signal-to-noise ratio and frequency-sampling rate affect the feasibility and accuracy of parameter estimation. We find that parameter estimation is feasible at frequency-sampling rates that are well below that suggested by the 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, thereby obtaining information about the surface on sub-resolution scales. The dissertation extends the model to describe marked point processes. We discover that ignoring the marks can cause significant estimation error when estimating the regularity model parameters in the presence of mark noise. Joint estimation of the regularity and mark parameters is feasible only when the variance of the marks is large with respect to their mean. Accounting for the marks can, however, allow the regularity parameters to be accurately estimated in the presence of mark noise.
Degree
Ph.D.
Advisors
Bell, Purdue University.
Subject Area
Electrical engineering|Remote sensing
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