The results presented in this dissertation concern two different types of tomographic
imaging. The first part of the dissertation is devoted to the time reversal method for
approximate reconstruction of images in thermoacoustic tomography. A thorough
numerical study of the method is presented. Error estimates of the time reversal
approximation are provided. In the second part of the dissertation a type of emission
tomography, called Compton camera imaging is considered. The mathematical
problem arising in Compton camera imaging is the inversion of the cone transform.
We present three methods for inversion of this transform in two dimensions. Numerical
examples of reconstructions by these methods are also provided. Lastly, we turn
to a problem of significance in homeland security, namely the detection of geometrically
small, low emission sources in the presence of a large background radiation.
We consider the use of Compton type detectors for this purpose and describe an
efficient method for detection of such sources. Numerical examples demonstrating
this method are also provided.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2010-08-8521 |
| Date | 2010 August 1900 |
| Creators | Georgieva-Hristova, Yulia Nekova |
| Contributors | Kuchment, Peter |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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