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 et. al. (see IEEE Nuclear Science Symposium and Medical Imaging Conference, Orlando, 1983) has presented a recursive, monotonically convergent and computationally efficient algorithm to invert sub-matrices of the FIM corresponding to a small region of interest in image reconstruction. The convergence rate of this algorithm depends on a splitting matrix which can be interpreted as a complete-data FIM. We investigate the acceleration of the algorithm using several different 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