| This thesis addresses the problem of analyzing the performance of a SPECT nuclear medical imaging system in the context of detection tasks. We propose a computationally efficient means for the prediction of the detectability with images reconstructed by a statistical method---a maximum a posteriori (MAP) Bayesian method. We also propose a computationally efficient method to evaluate the local point spread function and variance of MAP reconstructions for a SPECT system. The work starts from the modeling of the system matrix of a SPECT system. The model of attenuation and depth-dependent blur of a SPECT system is discussed in detail. Their differences from a PET system are emphasized. After modeling the system matrix, reconstruction methods are described, especially the MAP method. We focus on a method to propagate noise from some acquired projection data to the reconstructions through the MAP reconstruction operator. The method is specifically designed for SPECT with the attenuation and depth-dependent blur modeled. A theoretical expression for evaluating the pixel-wise standard deviation of MAP reconstructions is derived. To validate the theory, a number of Monte Carlo simulations have been conducted. The results of pixel-wise standard deviation from both our theoretical method and Monte Carlo simulations show good agreement. To predict the detectability in a detection task, we study the performance of two numerical observers, a Hotelling observer and Channelized Hotelling observer (CHO). The CHO is commonly used to emulate human observers. An efficient method to predict detectability is proposed and the results are validated with Monte Carlo simulations. Finally, we address the future work to be done. |
