The University of Arizona Campus Repository
>
UA Graduate and Undergraduate Research
>
UA Theses and Dissertations
>
Dissertations
>

# 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:
- Issue Date:
- 2016
- Publisher:
- 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:
- Degree Name:
- Ph.D.
- Degree Level:
- doctoral
- Degree Program:
- Degree Grantor:
- University of Arizona
- Advisor:

# Full metadata record

DC Field | Value | Language |
---|---|---|

dc.language.iso | en_US | en |

dc.title | Analytical Study and Numerical Solution of the Inverse Source Problem Arising in Thermoacoustic Tomography | en_US |

dc.creator | Holman, Benjamin Robert | en |

dc.contributor.author | Holman, Benjamin Robert | en |

dc.date.issued | 2016 | - |

dc.publisher | The University of Arizona. | en |

dc.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. | en |

dc.description.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. | en |

dc.type | text | en |

dc.type | Electronic Dissertation | en |

dc.subject | inverse source problem | en |

dc.subject | optoacoustic tomography | en |

dc.subject | thermoacoustic tomography | en |

dc.subject | tomography | en |

dc.subject | wave equation | en |

dc.subject | Applied Mathematics | en |

dc.subject | inverse problem | en |

thesis.degree.name | Ph.D. | en |

thesis.degree.level | doctoral | en |

thesis.degree.discipline | Graduate College | en |

thesis.degree.discipline | Applied Mathematics | en |

thesis.degree.grantor | University of Arizona | en |

dc.contributor.advisor | Kunyansky, Leonid A. | en |

dc.contributor.committeemember | Brio, Moysey | en |

dc.contributor.committeemember | Indik, Robert | en |

dc.contributor.committeemember | Gillette, Andrew | en |

dc.contributor.committeemember | Kunyansky, Leonid A. | en |

All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.