Markov-chain Monte Carlo for the performance of a channelized-ideal observer in detection tasks with non-Gaussian lumpy backgrounds

The Bayesian ideal observer is optimal among all observers and sets an upper bound for observer performance in binary detection tasks.(1) This observer provides a quantitative measure of diagnostic performance of an imaging system, summarized by the area under the receiver operating characteristic curve (AUC),(1) and thus should be used for image quality assessment whenever possible. However, computation of ideal-observer performance is difficult because this observer requires the full description of the statistical properties of the signal-absent and signal-present data, which are often unknown in tasks involving complex backgrounds. Furthermore, the dimension of the integrals that need to be calculated for the observer is huge. To estimate ideal-observer performance in detection tasks with non-Gaussian lumpy backgrounds, Kupinski et al.(2) developed a Markov-chain Monte Carlo (MCMC) method, but this method has a disadvantage of long computation times. In an attempt to reduce the computation load and still approximate ideal-observer performance, Park et al.(3,4) investigated a channelized-ideal observer (CIO) in similar tasks and found that the CIO with singular vectors of the imaging system approximated the performance of the ideal observer. But, in that work, an extension of the Kupinski MCMC was used for calculating the performance of the CIO and it did not reduce the computational burden. In the current work, we propose a new MCMC method, which we call a CIO-MCMC, to speed up the computation of the CIO. We use singular vectors of the imaging system as efficient channels for the ideal observer. Our results show that the CIO-MCMC has the potential to speed up the computation of ideal observer performance with a large number of channels.