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Sparsity and Compressed Sensing for Electromagnetic Scattering and Radiation Applications
O'Donnell, Andrew Nickerson

2014, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
Real-world electromagnetics problems often involves analysis from electrically large structures. Accurate knowledge of the radar signature of targets is needed for many applications within the defense community. Such applications include target recognition and systems analysis. Finding a complete radar signature for a large target requires a large amount of data over frequency and aspect angle to satisfy the Nyquist sampling criterion. Fortunately, the scattering from electrically large targets often comes from a small set of localized target features. This characteristic invites the use of sparsity and Compressed Sensing to alleviate the amount of data needed to characterize a target.
State of the art models based on high-frequency asymptotic physics use scattering centers that scale as a half-power of frequency, but many scattering features on real world targets do not follow this model. A more general model is proposed here that combines physical basis functions with a polynomial basis resulting in a robust representation that is able to compress scattering centers with various types of frequency dependencies for very wide bandwidths. This mixed basis is extended to include angular variations which allows for simultaneous radar signature compression in frequency and angle. Additionally, this model resolves two issues that plague automated scattering center compression algorithms, namely grid mismatch and merged scattering centers caused by resolution limits. Because we have a sparse representation for the radar signature, Compressed Sensing theory can be applied to acquire the scattering center representation with minimal sampled data. It is shown that the mixed basis is able to acquire the scattering center representation through Compressed Sensing with significantly less samples compared to other scattering center models.

In addition to electromagnetic scattering applications, this dissertation investigates sparsity and Compressed Sensing for large aperture radiation and for computational electromagnetics. For electrically large apertures, very fine sampling is needed to distinguish the peaks and nulls of the radiation pattern. However, the radiation from each point source on the edge is a slowly varying function of angle that can be expanded via a low-order polynomial. Given this sparse representation, Compressed Sensing is used to find the radiation pattern with significantly less samples.
Sparsity and Compressed Sensing are investigated for reducing the numerical cost of integral equation solvers within the field of computational electromagnetics. With Method of Moments, the matrix interactions between separated groups is low rank which allows for an efficient factorization of the block matrix containing the interactions. However, the rank depends on the physical size of the groups, their separation distance, and the frequency. For electrically large targets, Method of Moments is still a slow process which prevents its usage for many real world applications. An investigation is performed to understand if sparse representations can be used to describe the interactions between groupings in Method of Moments.
Robert Burkholder (Advisor)
Joel Johnson (Committee Member)
Fernando Teixeira (Committee Member)
243 p.

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O'Donnell, A. (2014). Sparsity and Compressed Sensing for Electromagnetic Scattering and Radiation Applications. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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O'Donnell, Andrew. "Sparsity and Compressed Sensing for Electromagnetic Scattering and Radiation Applications." Electronic Thesis or Dissertation. Ohio State University, 2014. OhioLINK Electronic Theses and Dissertations Center. 23 Nov 2017.

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O'Donnell, Andrew "Sparsity and Compressed Sensing for Electromagnetic Scattering and Radiation Applications." Electronic Thesis or Dissertation. Ohio State University, 2014. https://etd.ohiolink.edu/

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Full text release has been delayed at the author's request until July 09, 2019