List-mode SPECT reconstruction using empirical likelihood

This dissertation investigates three topics related to imagereconstruction from list-mode Anger camera data. Our mainfocus is the processing of photomultiplier-tube (PMT)signals directly into images. First we look at the use of list-mode calibration data toreconstruct a non-parametric likelihood model relating theobject to the data list. The reconstructed model can thenbe combined with list-mode object data to produce amaximum-likelihood (ML) reconstruction, an approach we calldouble list-mode reconstruction. This trades off reducedprior assumptions about the properties of the imaging systemfor greatly increased processing time and increaseduncertainty in the reconstruction. Second we use the list-mode expectation-maximization (EM)algorithm to reconstruct planar projection images directlyfrom PMT data. Images reconstructed by EM are compared withimages produced using the faster and more common techniqueof first producing ML position estimates, then histogramingto form an image. A mathematical model of the human visualsystem, the channelized Hotelling observer, is used tocompare the reconstructions by performing the Rayleigh task,a traditional measure of resolution. EM is found to producehigher resolution images than the histogram approach,suggesting that information is lost during the positionestimation step. Finally we investigate which linear parameters of an objectare estimable, in other words may be estimated without biasfrom list-mode data. We extend the notion of a linearsystem operator, familiar from binned-mode systems, tolist-mode systems, and show the estimable parameters aredetermined by the range of the adjoint of the systemoperator. As in the binned-mode case, the list-modesensitivity functions define ``natural pixels'' with whichto reconstruct the object