Analysis of signal detectability in statistically reconstructed tomographic images

Imaging in general, and emission tomography in particular, has become an important tool in many areas of medical diagnosis. Several common applications of emission tomography, such as the diagnosis of lung tumors or myocardial perfusion defects, involve the detection of a spatially localized target signal in an image reconstructed from noisy data. Such detection tasks are affected by various design parameters of the imaging system and reconstruction algorithm. This thesis is concerned with optimizing regularized image reconstruction methods for emission tomography with respect to the detectability of a spatially localized target signal in the reconstructed images.; We first consider the task of detecting a statistically varying signal of known location on a statistically varying background in a reconstructed tomographic image. We show that a broad family of linear observer models can achieve exactly optimal detection performance in this task if one chooses a suitable reconstruction method. This conclusion encompasses several well-known models from the literature, including those with a frequency-selective channel mechanism. Interestingly, the "optimal" linear reconstruction methods for many of these observer models are unregularized and in some cases quite unconventional. In the case of channelized models in particular, the observer's ability to prewhiten determines the extent to which its detection performance can benefit from regularization. That is, regularization is more important for channelized observers that have incomplete knowledge of the second-order statistics of the reconstructed images.; Subsequently, we investigate detection tasks where the location of the target signal is unknown to the observer. This location uncertainty complicates the mathematical analysis of observer performance significantly. We consider model observers whose decisions are based on the maximum value of a linear local test statistic over all possible signal locations. Several of our conclusions about the known-location task extend to this case. Previous approaches to this problem have used Monte Carlo simulations to evaluate the localization performance of maximum-statistic observers. We propose an alternative approach, where approximations of tail probabilities for the maximum of correlated Gaussian random fields facilitate analytical evaluation of detection performance. We illustrate how these approximations can be used to optimize the probability of detection (at low probabilities of false alarm) for the observers of interest.