On the use of physical basis functions in a sparse expansion for electromagnetic scattering signatures

Abstract

Radar images are created from measurements of the electromagnetic field scattered from an object or scene of interest. The scattered field defines the radar signature as a function of frequency and aspect angle. High resolution radar images and radar signatures are used for target recognition, tracking, and hardware-in-the-loop testing. High resolution radar images of electrically large targets may require a large amount of data to be measured, stored, and processed. A sparse representation of this data may allow the radar signature to be efficiently measured, stored, and rapidly reconstructed on demand.Compressed sensing is applied to obtain the sparse representation without measuring the full data set. "Compressed sensing" has different interpretations, but in this thesis it refers to using non-adaptive, random samples of the measured signal, with no a priori knowledge of the signal. According to compressed sensing theory, this is possible if the radar signature can be expressed in terms of a sparse basis. If a signal can be approximated by K non-zero coefficients in the sparse basis ("K-sparse"), the coefficients may be obtained with random sampling of the signal at sub-Nyquist rates provided that K is much smaller than the total number of Nyquist samples. The random sampling is nonadaptive (i.e., future samples are independent of previous samples) and the number of iii samples required is primarily related to the sparseness of the signal, and not the bandwidth nor the size of the dictionary from which the basis functions are selected.The objective of this thesis is to investigate the effectiveness of physical basis functions, defined as point scatter functions with frequency-dependent amplitudes characteristic of physical scattering mechanisms, to provide an improved sparse basis in which to expand radar signatures. The goal is to represent a radar signature accurately with the fewest terms possible and with the fewest measurements. Use of physical basis functions also provides insight into the scattering mechanism that is the source of the scattering. If the scattering mechanism is not known a priori or if a combination of scattering mechanisms is present in a single scattering center, a combined physical basis function is shown to provide a much more efficient representation. The angular dependence, which is usually not as simple as the frequency dependence, is incorporated using a low-order polynomial defined over limited angular sectors.The closed-form physical optics solution for the far-field electromagnetic backscatter from flat perfect electrically conducting plates is used to demonstrate the form of the physical basis functions and their efficacy as a sparse basis in which to expand the scattered signal. The coefficients of the physical basis functions are found using the Orthogonal Matching Pursuits algorithm to solve the -minimization problem.