A Vector Uniform Cramer-Rao Bound for SPECT System Design

In this paper, we present the use of modified uniform Cramer-Rao type bounds (MUCRB) for the design of single photon emission tomography (SPECT) systems. The MUCRB is the lowest attainable total variance using any estimator of an unknown vector parameter, whose mean gradient matrix satisfies a given constraint. Since the mean gradient is closely related to local impulse function, the MUCRB approach can be used to evaluate the fundamental tradeoffs between spatial resolution and variance that are achievable with a given SPECT system design. As a possible application, this approach allows one to compare different SPECT system designs based on the optimum average resolution-variance tradeoffs that can be achieved across multiple control-points inside a region-of-interest. The formulation of the MUCRB allows detailed modelling of physical aspects of practical SPECT systems and requests only a modest computation load. It can be used as an analytical performance index for comparing different SPECT system or aperture designs.