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Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this correspondence, we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient algorithms. For a large class of inverse problems, we show that nonmonotone Gauss-Seidel and preconditioned conjugate gradient algorithms require significantly fewer flops for convergence than monotone "bound preserving" algorithms.

Specifying the system matrix is one of the most important processes in computed tomography. For SPECT, the imaging physics can be very difficult to model and approximations are made which result in mismatch between the model and the data. In a move toward better modeling the physics, we developed a Monte Carlo method for specifying the system matrix for small animal imaging (but is also applicable for human imaging). A study was performed using the computergenerated MOBY rat phantom. This phantom returns a high resolution (0.90 mm) transmission map, which was used in Monte Carlo simulations to estimate attenuation and scatter. System matrices were estimated for the reconstruction of 6 heart slices from projections of 6 detector rows. SimSET was used to model 3 system matrices for each of the following: no attenuation and no scatter, attenuation only, and attenuation and scatter. For each slice, the system matrices had 4096=64x64 columns each representing a sinogram from a different source voxel in the slice. SimSET simulated 10 6 counts for each source voxeI. Each simulated 140 keY photon was forced to be detected on one of the 180 parallel projections evenly spaced over 360°. The system matrices also modeled spillover to account for the scatter from outside the 6 heart slices. For the reconstruction, projections were simulated using SimSET (10 12 total counts) to estimate the projection of the 6 slices including scatter from outside the 6 slices. These projections were reconstructed using the estimated system matrices and using 50 iterations of the ML-EM algorithm. There was a 20% increase of average intensity over the heart region with attenuation correction compared to without attenuation correction and a 3.5% decrease from the attenuation corrected result after scatter + attenuation correction.Attenuation correction reconstruction alone, overestimated the original by 3.3%. The results suggest that for quantitative small animal imaging it is important to correct for both attenuation and scatter when using radiolabeled tracers that emit 140 keY photons. This is even more true for radiolabeled tracers that emit 27.5 keY photons as both attenuation and scatter are more important at that lower energy.

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