Objective assessment of image quality through task-specific metrics has a long history in medical imaging and is regarded by many as ultimately being the most meaningful approach to medical image evaluation.^{1}^{–}^{4} However, the application of task-based assessment to x-ray computed tomography (CT) is recent relative to its application to planar imaging modalities and nuclear medicine. One reason for this delay is that metrics based on the Hotelling observer (HO),^{3} such as those considered in this work, involve the image covariance matrix, and in CT, this matrix is often extremely large (well over $109$ elements), poorly conditioned, and possesses few, if any, simplifying structural properties. In order to address the challenge of large dimensionality, efficient channels have been proposed^{5}^{–}^{7} which essentially constitute a transformation of the image into a new basis, where the number of basis functions is substantially less than the number of image pixels. Another common means of circumventing the dimensionality problem is to assume noise stationarity, so that HO metrics can be obtained with relative computational efficiency through discrete Fourier transform (DFT) operations (see Sec. 2). Meanwhile, in order to address the somewhat unpredictable structure of the image covariance, various estimation strategies have been proposed which rely on samples of noisy images in order to construct an estimate for the image covariance when an analytic formulation of image covariance is impossible or infeasible.^{8}^{,}^{9}