Analytical Study and Numerical Solution of the Inverse Source Problem Arising in Thermoacoustic Tomography

Persistent Link:
http://hdl.handle.net/10150/612954
Title:
Analytical Study and Numerical Solution of the Inverse Source Problem Arising in Thermoacoustic Tomography
Author:
Holman, Benjamin Robert
Issue Date:
2016
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
In recent years, revolutionary "hybrid" or "multi-physics" methods of medical imaging have emerged. By combining two or three different types of waves these methods overcome limitations of classical tomography techniques and deliver otherwise unavailable, potentially life-saving diagnostic information. Thermoacoustic (and photoacoustic) tomography is the most developed multi-physics imaging modality. Thermo- and photo-acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods cannot be used. In chapter 2 we present a fast iterative reconstruction algorithm for measurements made at the walls of a rectangular reverberant cavity with a constant speed of sound. We prove the convergence of the iterations under a certain sufficient condition, and demonstrate the effectiveness and efficiency of the algorithm in numerical simulations. In chapter 3 we consider the more general problem of an arbitrarily shaped resonant cavity with a non constant speed of sound and present the gradual time reversal method for computing solutions to the inverse source problem. It consists in solving back in time on the interval [0, T] the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.
Type:
text; Electronic Dissertation
Keywords:
inverse source problem; optoacoustic tomography; thermoacoustic tomography; tomography; wave equation; Applied Mathematics; inverse problem
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Kunyansky, Leonid A.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleAnalytical Study and Numerical Solution of the Inverse Source Problem Arising in Thermoacoustic Tomographyen_US
dc.creatorHolman, Benjamin Roberten
dc.contributor.authorHolman, Benjamin Roberten
dc.date.issued2016-
dc.publisherThe University of Arizona.en
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en
dc.description.abstractIn recent years, revolutionary "hybrid" or "multi-physics" methods of medical imaging have emerged. By combining two or three different types of waves these methods overcome limitations of classical tomography techniques and deliver otherwise unavailable, potentially life-saving diagnostic information. Thermoacoustic (and photoacoustic) tomography is the most developed multi-physics imaging modality. Thermo- and photo-acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods cannot be used. In chapter 2 we present a fast iterative reconstruction algorithm for measurements made at the walls of a rectangular reverberant cavity with a constant speed of sound. We prove the convergence of the iterations under a certain sufficient condition, and demonstrate the effectiveness and efficiency of the algorithm in numerical simulations. In chapter 3 we consider the more general problem of an arbitrarily shaped resonant cavity with a non constant speed of sound and present the gradual time reversal method for computing solutions to the inverse source problem. It consists in solving back in time on the interval [0, T] the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.en
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectinverse source problemen
dc.subjectoptoacoustic tomographyen
dc.subjectthermoacoustic tomographyen
dc.subjecttomographyen
dc.subjectwave equationen
dc.subjectApplied Mathematicsen
dc.subjectinverse problemen
thesis.degree.namePh.D.en
thesis.degree.leveldoctoralen
thesis.degree.disciplineGraduate Collegeen
thesis.degree.disciplineApplied Mathematicsen
thesis.degree.grantorUniversity of Arizonaen
dc.contributor.advisorKunyansky, Leonid A.en
dc.contributor.committeememberBrio, Moyseyen
dc.contributor.committeememberIndik, Roberten
dc.contributor.committeememberGillette, Andrewen
dc.contributor.committeememberKunyansky, Leonid A.en
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