On reconstruction methods and image quality in emission tomography

In this thesis, I shall address two important practical issues in emission tomographic imaging systems such as SPECT and PET, namely, efficient methods of image reconstruction and efficient methods for task-based image quality assessment, and a third theoretical issue that arises in the task-based assessment of image quality.; The first problem is that of fast and accurate emission tomographic image reconstruction. It is widely known that list-mode data acquisition offers higher levels of precision and can lead to more accurate image reconstruction than binned-mode data acquisition. However, there is a dearth of fast globally convergent reconstruction methods for list-mode data. We propose a fast, globally convergent, ordered subset, list-mode reconstruction method based on an incremental EM (expectation maximization) technique and demonstrate the efficacy of our method via simulations.; The second problem involves efficient methods for analyzing the performance of emission tomography systems on detection tasks. Performance indices for detection tasks are widely accepted as measures of image quality in PET and SPECT. However, evaluating these performance indices is often too computationally expensive. Rapid means are available to compute performance indices only for simplified detection tasks not involving signal location uncertainty. But performance indices on such simplified detection tasks may not accurately reflect the differences in quality in two imaging systems. Here, we propose a rapid means to evaluate performance indices on detection tasks involving signal location uncertainty. We compare our rapid techniques to conventional techniques via simulations and demonstrate that a two orders of magnitude speed-up is obtained by our method with negligible loss in accuracy. We use our rapid techniques to determine optimal smoothing in emission tomography. We also propose new rapid techniques for computing detection performance indices that account for the noise due to scattered photons in SPECT.; The third problem involves the development of decision strategies that maximize a popular performance index for detection tasks involving location uncertainty, the area under the LROC (localization receiver operating characteristic) curve. We develop decision strategies that maximize the area under the LROC curve and also analyze these decision strategies from a Bayes risk perspective.