Direct estimation and correction of bias from temporally variable non-stationary noise in a channelized Hotelling model observer

Abstract

Channelized Hotelling model observer (CHO) methods were developed to assess performance of an x-ray angiography system. The analytical methods included correction for known bias error due to finite sampling. Detectability indices () corresponding to disk-shaped objects with diameters in the range 0.5–4 mm were calculated. Application of the CHO for variable detector target dose (DTD) in the range 6–240 nGy frame−1 resulted in estimates which were as much as 2.9× greater than expected of a quantum limited system. Over-estimation of was presumed to be a result of bias error due to temporally variable non-stationary noise. Statistical theory which allows for independent contributions of ‘signal’ from a test object (o) and temporally variable non-stationary noise (ns) was developed. The theory demonstrates that the biased is the sum of the detectability indices associated with the test object and non-stationary noise (). Given the nature of the imaging system and the experimental methods, cannot be directly determined independent of . However, methods to estimate independent of were developed. In accordance with the theory, was subtracted from experimental estimates of , providing an unbiased estimate of . Estimates of exhibited trends consistent with expectations of an angiography system that is quantum limited for high DTD and compromised by detector electronic readout noise for low DTD conditions. Results suggest that these methods provide estimates which are accurate and precise for . Further, results demonstrated that the source of bias was detector electronic readout noise. In summary, this work presents theory and methods to test for the presence of bias in Hotelling model observers due to temporally variable non-stationary noise and correct this bias when the temporally variable non-stationary noise is independent and additive with respect to the test object signal.