Signal detection with random backgrounds and random signals
In this dissertation we explore theoretical and computational methods to investigate Bayesian ideal observers for performing signal-detection tasks. Object models are used to take into account object variability in image backgrounds and signals for the detection tasks. In particular, lumpy backgrounds (LBs) and Gaussian signals are used for various paradigms of signal-detection tasks. Simplified pinhole imaging systems in nuclear medicine are simulated for this work. Markov-chain Monte Carlo (MCMC) methods that estimate the ideal observer test statistic, the likelihood ratio, for signal-known-exactly (SKE) tasks, where signals are nonrandom, are employed. MCMC methods are extended to signal-known-statistically (SKS) tasks, where signals are random. Psychophysical studies for the SKE and SKS tasks using non-Gaussian and Gaussian distributed LBs are conducted. The performance of the Bayesian ideal observer, the human observer, and the channelized-Hotelling observer for the SKE and SKS tasks is compared. Human efficiencies for both the SKE tasks and SKS tasks are estimated. Also human efficiencies for non-Gaussian and Gaussian-distributed LBs are compared for the SKE tasks. Finally, the theory of the channelized-ideal observer (CIO) is introduced to approximate the performance of the ideal observer by the performance of the CIO in cases where the channel outputs of backgrounds and signals are non-Gaussian distributed. Computational approaches to estimate the CIO are investigated.