Maximum likelihood estimation maximization deconvolution in spatial and combined spatial- energy domains for a detector array system

In previous work, our research group has developed gamma-ray imaging methods using two-interaction Compton events recorded from a single 1.5 cm x 1.5 cm x 1 cm 3D position-sensitive CdZnTe detector. The first of these is a maximum likelihood estimation maximization (MLEM) algorithm to estimate the spatial source distribution from measured events. The other, energy-imaging integrated spectral deconvolution, takes place in integrated spatial and energy space using the MLEM algorithm, allowing it to deconvolve the source image at any specific energy, as well as the spectrum for any specific direction. By including Compton-scattering events in the system model, it also estimates the true incident gamma-ray spectrum from each direction free of the Compton continuum. In order to improve efficiency at high energies as well as angular resolution, a new system (Polaris) is under construction using two layers of 3 x 3 modular 3D CdZnTe detectors, each with dimensions of 2 cm x 2 cm x 1.5 cm. Both MLEM methods, which used two-interaction Compton events, have been generalized to the new array system. Moreover, the system response function for both methods have been extended to make use of three-interaction events occurring in the system. The system response function for MLEM in the spatial domain has also been extended to use single-interaction events. Since it is impossible to pre-calculate the system response function due to the large number of possible events, analytic formulas are derived to allow the calculation of the system response function as reconstruction occurs. Finally, representative results are presented.