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Reconstruction and convergence of anisotropic conductivity tensors using magneto-acoustic tomography with magnetic induction
Dissertation   Open access

Reconstruction and convergence of anisotropic conductivity tensors using magneto-acoustic tomography with magnetic induction

Isaac Woods
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2024
DOI:
https://doi.org/10.17918/00010688
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Abstract

Finite element method--Study and teaching Inverse problems (Differential equations) Differential equations, Partial Scientific computing Numerical Analysis
Magneto-Acoustic Tomography with Magnetic Induction (MAT-MI) is a novel hybrid imaging modality for reconstructing the conductivity map of a conductive object. It is a two-step process in which a physical scan is first taken to determine the object's internal acoustic source data. This data is utilized in the second step of MAT-MI to reconstruct the object's conductivity map through a two-step quasi-Newton algorithm. In this work, suitable conditions for convergence of reconstruction algorithms are established in the cases of isotropic conductivity and various forms of anisotropic conductivities. In addition, an extended algorithm for reconstructing full anisotropic conductivity tensors using the MAT-MI process is proposed. An associated convergence result is established using a fixed-point argument. Each section ends with a gallery of computational experiments and a brief discussion of the numerical methods used to produce them.

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