Compton camera imaging and the cone transform: a brief overview**This work was supported in part by NSF DMS grants 1211463 (the first two authors), 1211521 and 141877 (the third author), as well as a College of Science of Texas A&M University grant.

Abstract

While most of Radon transform applications to imaging involve integrations over smooth sub-manifolds of the ambient space, lately important situations have appeared where the integration surfaces are conical. Three of such applications are single scatter optical tomography, Compton camera medical imaging, and homeland security. In spite of the similar surfaces of integration, the data and the inverse problems associated with these modalities differ significantly. In this article, we present a brief overview of the mathematics arising in Compton camera imaging. In particular, the emphasis is made on the overdetermined data and flexible geometry of the detectors. For the detailed results, as well as other approaches (e.g. smaller-dimensional data or restricted geometry of detectors) the reader is directed to the relevant publications.Only a brief description and some references are provided for the single scatter optical tomography.