| Summary: | In single-photon emission computed tomography (SPECT), the goal is to estimate the biodistribution of radioactive pharmaceuticals that have been administered to a patient. Various degrading physical effects contribute to inaccuracies in the estimation process. In this dissertation, we examine the effects of photon attenuation and noisy projection data on SPECT image reconstructions. In addition, image-quality assessment is performed to determine the best reconstruction method for a given detection task. Accurate quantitation of the activity distribution is desirable for detection and estimation tasks in SPECT. Photon attenuation hinders our ability to obtain good quantitative estimates; therefore effective correction techniques need to be developed. For the case of a convex body outline and a uniformly attenuating medium, the attenuation problem is modelled by the exponential Radon transform. In this dissertation, we mathematically describe the three, previously published, analytical inverses to this forward problem, known as the methods of Bellini, Inouye, and Tretiak & Metz. Also included are a new analytic inverse developed recently by Metz and the widely used approximate inverse of Chang. The physical properties of photon decay and collection cause random fluctuations to be introduced into the measured projection data. During the reconstruction process, the noise structure is altered by filtering and backprojection. By characterizing the noise in the reconstructions, optimal reconstruction and restoration filters may be derived. In this study, we examine the behavior of the noise as propagated through the attenuation correction and reconstruction process for a uniformly emitting and attenuating disk object. The results demonstrate that SPECT image noise is globally nonstationary, although it is locally stationary at the center of the disk for the Bellini, Chang, Scaled Filtered-Backprojection, new Metz, and Tretiak & Metz methods. The Inouye method yielded the highest noise variance at the disk's center, while the Tretiak & Metz method increased noise variance drastically toward the edge of the disk. In addition to noise characterization, we seek the best attenuation correction method for clinical use. Image quality is defined by the ability of an observer to perform a specified task given a class of images. Psychophysical studies were performed with human observers for the tasks of detecting a 10% contrast cold disk signal on a uniformly emitting and attenuating circular background, where the signal was located either at the center or near the edge of the disk. The ideal, non-prewhitening and region-of-interest model observers were evaluated as image-quality measures, with the goal of finding an observer that correlated well with human performance. For the center-location task, we found that the human observers did not perform significantly better with any particular method. Also, the model observers were shown to be invariant across correction method. For the edge-location task, the human observers performed statistically significantly worse with the method of Tretiak & Metz. This behavior was also reflected in the non-prewhitening and region-of-interest model-observer signal-to-noise ratios.
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