Assessment of CT Image Quality Using a Bayesian Framework

In computed tomography, there is a tradeoff between the quality of the reconstructed image and the radiation dose received by the patient. In order to find an appropriate compromise between the image quality of the reconstructed images and the radiation dose, it is important to have reliable methods for evaluating the quality of the reconstructed images. A successful family of methods for the assessment of image quality is task-based image quality assessment, which often involves the use of model observers, and which assesses the quality of the image reconstruction by deriving a figure of merit. Here, we present a Bayesian framework that can be used in task-based image quality assessment. Our framework is applicable to binary classification problems with normally distributed observations, and we make the additional assumption that the covariance matrix is the same in both image classes. We choose a particular non-informative prior for the parameters of our model, which allows us to derive an expression for the Bayes factor for the binary classification problem which to the best of our knowledge is novel. We introduce a novel model observer based on this Bayes factor. Further, we have developed a methodology for estimating the posterior distribution of the figure of merit for this type of classification problem. Compared with classical statistical approaches, our Bayesian approach has the advantage that it provides a full characterization of the uncertainty of the figure of merit. Our choice of prior allows us to design a simple Monte Carlo algorithm to efficiently sample the posterior of the figure of merit of the ideal observer, in contrast to common Bayesian procedures which rely on computationally expensive Markov chain Monte Carlo sampling. We have shown that for training samples of sufficient size, our estimated credible intervals for the figure of merit have coverage probabilities close to their credibility, so that our approach can reasonably be used within a classical statistical framework as well.