Hemispherical spatial sampling study and 3D image reconstruction using iterative algorithms for a Compton SPECT camera model

In this paper we will present numerical studies of the performance of a 3D Compton camera being developed at the University of Michigan. We present a physical model of the camera which exploits symmetries by using an adapted spatial sampling pattern in the object domain. This model increases the sparsity of the transition matrix to reduce the very high storage and computation requirements. This model also allows the decomposition of the transition matrix into several small blocks that are easy to store. We also present the transition matrix of our system analytically computed with a real time algorithm. We geometrically optimize our hemispherical sampling and develop a 3D volumetric interpolation. Finally, we present a 3D image reconstruction method which uses the Gauss-Seidel algorithm to minimize a penalized least square objective