The mutual information criterion for SPECT aperture evaluation and design

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Abstract
An aperture performance criterion for single-photon-emission computed tomography (SPECT) that is based on the mutual information (MI) between the source and detector processes is proposed. The MI is a measure of the reduction in uncertainty of the emitter location, given the detector data, and it takes account of the inherent tradeoffs between the effects of sensitivity and resolution on source estimation accuracy. Specific expressions for the MI are derived for one-dimensional linear geometries and two-dimensional, parallel-slice, ring geometries under the assumptions of Poisson emission times, uniform emission angles, no scattering, and a known lost-count correction factor. For one-dimensional geometries a necessary and sufficient condition for an aperture to maximize the mutual information is given. The MI-optimal apertures are derived for various source distributions using an iterative maximization procedure. The MI is then numerically calculated for various ring apertures associated with the parallel-slice SPRINT II system.