Recursive CR bounds: algebraic and statistical acceleration

Computation of the Cramer-Rao bound involves inversion of the Fisher information matrix (FIM). The inversion can become computationally intractable when the number of unknown parameters is large. Hero has presented a re-cursive, monotonically convergent and computationally ef-cient algorithm to invert sub-matrices of the FIM corresponding to a small region of interest in image reconstruction 1]. The convergence rate of this algorithm depends on a splitting matrix which can be interpreted as a complete data FIM. In this paper we investigate the acceleration of the algorithm using several diierent choices of the complete-data FIM. We also present a conjugate gradient based algorithm which achieves a much faster convergence rate at the expense of monotone convergence. We apply the methods developed in this paper to emission tomography.