Analytic reconstruction for single photon emission computed tomography

This dissertation concentrates on improving analytical reconstruction algorithms for single photon emission computed tomography (SPECT).; In SPECT imaging, photon attenuation within the body is a major factor contributing to the quantitative inaccuracy in measuring the distribution of radioactivity. Thus, attenuation compensation is a major goal in SPECT development.; Among two-dimensional (2D) parallel-beam image reconstruction methods, Metz and Pan's 2D parallel-beam quasi-optimal method has superior noise properties. In this dissertation, analytical fan-beam and cone-beam algorithms are developed by extending Metz and Pan's parallel-beam quasi-optimal method. It is shown that these new algorithms also have good noise properties.; This dissertation also develops an image reconstruction algorithm for 180° data acquisition based on Metz and Pan's quasi-optimal method. This algorithm reconstructs the image with parallel-beam projection data acquired over a 180° view range.; In cone-beam planar-trajectory imaging, axial artifacts result from incomplete projection data. A skew-slit collimator system, which is a generalized cone-beam system, is introduced to reduce the axial artifacts without decreasing the transaxial spatial resolution. An image reconstruction algorithm is developed for this skew-slit system. This algorithm also has good noise properties, because it is based on Metz and Pan's quasi-optimal method.