"Mathematical problems of Thermoacoustic and Compton Camera Imaging,"
Ph.D. thesis, Department of Mathematics, Texas A&M University, College Station, TX (2010).
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. See Document
Associated Project(s):SHIELD (Smuggled HEU Interdiction through Enhanced anaLysis and Detection): A Framework for Developing Novel Detection Systems Focused on Interdicting Shielded HEU