Detection and discrimination of known signals in inhomogeneous, random backgrounds

Two studies of the effect of background inhomogeneity on observer performance in radionuclide emission imaging are presented. In the first, the task is detection of a Gaussian blob, and the imaging aperture is a pinhole of Gaussian profile. In the second, a simple discrimination task called the Rayleigh task is considered, and the aperture has a rectangular profile. In both cases performance of a suboptimal linear observer is calculated; in the first study the observer is one derived in a classic paper by Harold Hotelling, while in the second study the observer is a simple non-prewhitening matched filter. In both studies an important variable is the aperture size, and a key question is whether a small aperture or compact point spread function is advantageous. The main result is that a large aperture may perform very well or even optimally with a spatially uniform background but fail badly when the background is nonuniform. Thus predictions of image quality based on stylized tasks with uniform background must be viewed with caution. Medical Imaging III: Image Formation (1989).