New Theoretical Results on Channelized Hotelling Observer Performance Estimation with Known Difference of Class Means

Task-based assessments of image quality constitute a rigorous, principled approach to the evaluation of imaging system performance. To conduct such assessments, it has been recognized that mathematical model observers are very useful, particularly for purposes of imaging system development and optimization. One type of model observer that has been widely applied in the medical imaging community is the channelized Hotelling observer (CHO). Since estimates of CHO performance typically include statistical variability, it is important to control and limit this variability to maximize the statistical power of image-quality studies. In a previous paper, we demonstrated that by including prior knowledge of the image class means, a large decrease in the bias and variance of CHO performance estimates can be realized. The purpose of the present work is to present refinements and extensions of the estimation theory given in our previous paper, which was limited to point estimation with equal numbers of images from each class. Specifically, we present and characterize minimum-variance unbiased point estimators for observer signal-to-noise ratio (SNR) that allow for unequal numbers of lesion-absent and lesion-present images. Building on this SNR point estimation theory, we then show that confidence intervals with exactly-known coverage probabilities can be constructed for commonly-used CHO performance measures. Moreover, we propose simple, approximate confidence intervals for CHO performance, and we show that they are well-behaved in most scenarios of interest.