Reconstruction of SPECT images using generalized matrix inverses

Generalized matrix inverses are used to estimate source activity distributions from single photon emission computed tomography (SPECT) projection measurements. Image reconstructions for a numerical simulation and a clinical brain study are examined. The photon flux from the source region and photon detection by the gamma camera are modeled by matrices which are computed by Monte Carlo methods. The singular value decompositions (SVDs) of these matrices give considerable insight into the SPECT image reconstruction problem and the SVDs are used to form approximate generalized matrix inverses. Tradeoffs between resolution and error in estimating source voxel intensities are discussed, and estimates of these errors provide a robust means of stabilizing the solution to the ill-posed inverse problem. In addition to its quantitative clinical applications, the generalized matrix inverse method may be a useful research tool for tasks such as evaluating collimator design and optimizing gamma camera motion.