Monte Carlo calculation of Fisher information and Cramer-Rao Bounds

The families of Cramer-Rao bounds (CRB) are useful for comparing performance of different medical imaging systems. They relate the inverse of the fisher information matrix (FIM) to lower bounds on the covariance matrix of - possibly regularized - reconstructions. However, it is often difficult to apply in applications with a high dimensional measurement space, since the inversion and multiplication of large matrices requires large computer memory and lengthy computation. Monte Carlo integration (MCI) and local shift-invariance properties, for the FFT can be used to simplify the inversion, are possible solutions to estimating the FIM and modified uniform Cramer-Rao bound (M-UCRB), respectively. Inevitably, the fidelity of the approximation to the M-UCRB is determined by errors in the calculated FIM, which are introduced by the finite number of samples used for MCI, and in the accuracy of the local spatial invariance assumption. This research examines the issue of error propagation due to the limited number of samples by studying the performance of simulated medical imaging system.