Inverse Problems Arising in Medical, LIDAR, and Homeland Security Imaging

Abstract

Several tasks in the fields of medicine and homeland security require the ability to detect weak signals under stymieing conditions. For instance, in medical imaging single photon emission computed tomography can be used for imaging tumors, but the dosage must be limited to minimize radiation damage to patient tissue. In the field of homeland security, there is significant interest in detecting shielded nuclear sources, e.g. illicit nuclear material being smuggled at a border crossing. Additionally, homeland security and defense agencies are interested in using light detection and ranging (LIDAR) for gathering geospatial intelligence on e.g. targets under forest cover. In this dissertation we discuss recent advances in the application and theory of Compton and LIDAR imaging which address these types of problems.

Compton imaging utilizes the Compton scattering effect to detect high energy photons using devices called Compton cameras. Compton cameras measure the (weighted) conical Radon transform (CRT) of the radiative source distribution function. The conical Radon transform maps a function to its integrals over surface cones. Compton cameras thus provide partial direction information without any attenuation of the signal, which makes them especially suited for detection of weak signals in the presence of strong noise. Compton cameras therefore have significant potential for use in medical and homeland security applications. In particular we detail recently published results on a convolutional neural network which exhibits high sensitivity and specificity at detecting shielded Uranium-238 embedded in complex cargo configurations. We also obtain a range description of the CRT over the space of smooth functions with compact support, a result of great theoretical importance for future study of the CRT.

A coincidence processing algorithm for Geiger-mode LIDAR developed in collaboration with the Engineer Research and Development Center Geospatial Research Laboratory is detailed. Numerical implementation results of the algorithm are presented with real data collected by the Geospatial Research Laboratory. This algorithm is highly parallelizable and provides high quality 3D images of LIDAR targets.