Fast Methods for Approximation of Resolution and Covariance for SPECT

Resolution and covariance predictors have been derived previously for penalized-likelihood estimators. These predictors can provide accurate approximations to the local resolution properties and covariance functions for tomographic systems given a good estimate of the mean measurements. However, when numerous evaluations are made repeatedly (as in penalty design or calculation of variance images), these predictors still require large amounts of computing time. In [1], we discussed methods for precomputing a large portion of the predictor for shift-invariant system geometries. In this paper, we generalize the efficient procedure discussed in [1] to shift-variant single photon emission computed tomography (SPECT) systems. This generalization relies on a new attenuation approximation and several observations on the symmetries in SPECT systems. These new general procedures apply to both 2D and fully-3D SPECT models, that may be either precomputed and stored, or written in procedural form.