Maximum-Likelihood Deconvolution in the Spatial and Spatial-Energy Domain for Events With Any Number of Interactions

In previous works, maximum-likelihood expectation-maximization deconvolution for two-interaction events within a single CdZnTe detector with dimensions of was implemented. This deconvolution method is capable of estimating the source image for each energy range as well as the incident spectrum for each direction around the detector. To improve the detection efficiency and the image resolution, we have built a four-detector array system; each detector has dimensions of . Using this detector-array system, from a Co-60 measurement, 41.5% of recorded events in the energy window from 1100 keV to 1200 keV are two-interaction events. The goal of this work is to increase the efficiency of this deconvolution algorithm by extending the calculation of the system response functions to events with other number of interactions. We first analytically extend the system response function calculation to three-interaction events by deriving the probability density function, considering the measurement noise, and integrating over the digitization and pixelation volume. The system response function is then simplified, modularized, and extrapolated to events with other numbers of interactions from an array system. By including events with any number of interactions in the system model, imaging makes use of all recorded events, and the angular resolution is improved. This deconvolution algorithm is applicable to any gamma-ray detector system that has the capability of recording 3D interaction location and energy deposition for each interaction.