Maximum Likelihood Reconstruction for a Prototype Electronically Collimated Single Photon Emission System

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Abstract
An electronic collimation system for SPECT imaging has been designed to provide improved detection efficiency over a mechanical collimator. A maximum likelihood estimator (MLE) is derived for this prototype electronically collimated system. The data is shown to be independent and Poisson distributed. For the low count rates typical in nuclear medicine the statistical fluctuations due to the Poisson process are significant. Consequently resolution in reconstructions using the linear formulations typical in x-ray computed tomography is limited by the resulting non-stationary noise. The MLE approach however incorporates the Poisson nature of the data directly in the reconstruction process and thus results in superior reconstructions than those obtained using a linear approach. Inclusion of noise effects in modeling the system is shown to guarantee the existence of a unique MLE solution. The EM algorithm is employed to find the MLE solution. The structure of the transition probability matrix obtained using a polar sampling raster is exploited to speed up the algorithm. Results of a comprehensive computer simulation are presented.

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