Mutual information optimization and evaluation of single photon emission computed tomography.

In this thesis we study the performance of Single Photon Emission Computed Tomography using concepts and techniques of information theory. Two specific tomographic tasks are considered: image reconstruction and image feature classification. For the image reconstruction problem we derive a necessary and sufficient condition for an aperture to be information optimal. The aperture is nearly a collimator over aperture regions of high fluence, hence sacrificing fluence for better resolution, while it is nearly transparent over regions of low fluence, hence sacrificing resolution for better fluence. Simulations are presented which show that the mutual information of conventional uniform parallel hole apertures can be significantly lower than the maximum achievable information using an optimal aperture. We then study the effect of count loss side information on the mutual information for the reconstruction problem. We derive a lower bound on the information gain achievable from using count corrections. This bound increases with a quantity, the information divergence, measuring spatial dependence of the probability of losing a count from a particular emitter location. It is established that if this spatial dependence is significant high gains can be achieved when the mean number of detected gamma-rays is low. In particular, this implies that count corrections side information can greatly improve performance in dynamic studies where the reconstruction of a time varying mean source distribution mandates multi-stage data acquisition over short time intervals. For the feature classification problem we study the channel cut-off rate which is related to the information transfer from the image features to the projections data. On the basis of the cut-off rate and the information theoretic Fano bound we propose a very simple approximation to the probability of classification error of the optimal Bayes classifier. For the special case of two features, i.e. detection, we determine by simulation that the approximation is quite close to the actual Bayes minimum probability of error. We then study apertures which minimize the minimum probability of error approximation by maximizing the cut-off rate. It is determined that the optimal detection aperture can be simply approximated by an aperture which is reconstruction optimal for the Bayes averaged source distribution.PhDApplied SciencesBiological SciencesBiomedical engineeringBiophysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128450/2/9014013.pd