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Thesis (M.S.)--Tufts University, 2021.
Submitted to the Dept. of Mathematics.
Advisor: Eric Quinto.
Committee: Fulton Gonzalez, and Christoph Borgers.
Keyword: Mathematics.
We study the microlocal analysis of an elliptical Radon transform with applications to synthetic aperture radar (SAR). In the model considered, the transmitter is fixed at the origin ... read morein the plane and the receiver moves along the unit circle. The resulting elliptical Radon transform $R$ is shown to be a Fourier integral operator acting on distributions with compact support in the punctured unit ball $X$. For SAR imaging in $X$, we propose a modified cutoff elliptical Radon transform $R_\varepsilon$ and a filtered backprojection algorithm $R_\varepsilon^t \Lambda R_\varepsilon$, where $\Lambda$ is a well-chosen second-order differential operator motivated by Lambda tomography. We prove that $R_\varepsilon^t \Lambda R_\varepsilon$ is a first-order Fourier integral operator, characterize singularities which are visible and invisible to this and related algorithms, and provide illustrative numerical examples.read less
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