Accurate computation of the Hotelling observer for the evaluation of image reconstruction algorithms in helical, cone-beam CT

A task-based method for evaluating cone-beam CT image reconstruction algorithms is proposed. The task is signal-known-exactly/background-known-exactly detection. The aim is to compute the efficiency of image reconstruction with respect to this task. The efficiency is the ratio of the square of the signal detectability by the ideal observer in the reconstructed image and in the projection data. As reconstruction, here, is a non-invertible linear operator, the efficiency is less than or equal to one. For the model used to describe the projection data the ideal observer is equivalent to the Hotelling observer. To obtain Hotelling observer performance, the Hotelling template is computed in both the projection data and reconstructed image domains. Under the assumption of uncorrelated noise, the data domain Hotelling template computation is straight-forward; however, its computation in the reconstructed image space is complicated by having a very large non-diagonal covariance. In this work, an efficient, accurate method is developed for evaluating the Hotelling template in the reconstructed image space in cone-beam CT. Obtaining this template, enables the accurate computation of the efficiency of the cone-beam CT image reconstruction algorithm.