Cramer-Rao bound and image representation in emission tomography

The Cramer-Rao (CR) lower bound on the error variances of image reconstruction in emission tomography is valuable in that it can be specified independent of the reconstruction algorithm. In addition to the variance lower bounds, the inverse Fisher information matrix of the multi-parameter CR bound also contains information on the spatial resolution of estimates which achieve the lower bound. In this work the minimum variance and spatial resolution information of the CR bound are used for the evaluation of different representations of the emission map. The emission map is represented here as the superposition of basis functions, which can be rectangular/pixel, Gaussian or Kaiser-Bessel. Square and hexagonal packing of these basis functions are also studied. How the lower bounds and spatial resolution varies spatially are illustrated with example objects. It is shown how the multi-parameter CR bound can be used as a yardstick for evaluating the performances of different representations of the emission map. It gives a useful theoretical limit on how well different representations can perform