Lower Bounds on the Mean Square Error in Emission Tomography for Different Image Approximations

| A lower bound on the mean square error (MSE) of image reconstruction in emission tomography is obtained and used in the evaluation of diierent image approximations. One component of the lower bound on the MSE is the Cram er-Rao (CR) bound on the error variance. The CR bound for diierent image approximations is derived by knowing how the CR bound is modiied when one is interested in some functions of the model parameters. The other component of the lower bound on the MSE is the square of the bias. The study of the lower bound on the MSE for diierent image approximations is the study of the tradeoo between bias and error variance. It is shown that the relative contribution of the two components changes for diierent image approximations, total number of counts and emission densities.