Date of Award
Fall 10-27-2025
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Electrical and Computer Engineering
First Advisor
James Richie
Second Advisor
Chung Lee
Third Advisor
Cristinel Ababei
Abstract
Non-radiating sources are current distributions that produce no observable field outside a bounded domain, and their existence introduces inherent non-uniqueness in source-based inverse formulations. While these components do not contribute to the far-field scattered data, they significantly influence the internal consistency and accuracy of reconstructed contrast sources. To address this challenge, the dissertation employs singular value decomposition (SVD) to separate the induced contrast source into radiating and non-radiating components. Subspace Optimization Method (SOM) is implemented to improve computational efficiency and reconstruction accuracy by targeting the most significant singular subspaces. Additionally, it proposes the use of both radiating and non-radiating components of the field, along with the exploitation of the null space of the forward operator, to develop a novel approach for studying contrast source reconstruction. A complete orthogonal set of non-radiating basis functions using cylindrical Bessel functions is used to analytically represent the null space components. This method enhances the ability to characterize hidden or weakly scattering inclusions that traditional techniques may overlook. Simulation results across various object sizes and permittivity contrasts reveal that omitting non-radiating modes leads to substantial degradation in spatial fidelity, especially near object boundaries. However, far-field measurements remain largely unaffected, validating the hidden nature of these sources. The findings demonstrate that incorporating non-radiating sources into reconstruction frameworks is critical for physically accurate imaging, particularly in high-resolution or limited data scenarios. This work contributes to the theoretical understanding and practical solution of inverse scattering problems by revealing the necessity of modeling both visible and nonvisible components of the contrast source. It offers foundational insights applicable to electromagnetic imaging.
Comments
Doctor of Philosophy (PhD)