Channelised Hotelling observer detectability index vs minimum detectable contrast for x-ray computed tomography

<i>Objective.</i>The aim of this study is to investigate the relation between two figures of merit for the low contrast resolution of computed tomography (CT) imaging systems, with the perspective of its use for acceptance and constancy testing.<i>Approach.</i>We use simulated data as well as 29 CT image datasets of the MITA body phantom CCT189 obtained using a previously published protocol, including CT devices from five different manufacturers and various image reconstruction methods. From these data, the detectability index<i>d</i>' is determined using the channelised Hotelling observer (CHO), which requires hundreds of images per setting. We compare<i>d</i>' to the minimum detectable contrast (MDC), a statistically defined measure of low contrast detectability, that can be determined using only few images per setting.<i>Main results.</i>For the CHO with circular symmetric DDOG (dense difference of Gaussians) channels,<i>d</i>' is proportional to the inverse of the product of MDC and the diameter of the object to be detected. The proportionality factor depends strongly on the texture of the noise.<i>Significance.</i>The findings provide the basis for the development of an acceptance and constancy test for CT low contrast resolution, making use of<i>d</i>'CHO and MDC.