Uncertainty Quantification of Inclusion Boundaries in the Context of X-Ray Tomography

In this work, we describe a Bayesian framework for reconstructing the boundaries of piecewise smooth regions in the X-ray computed tomography (CT) problem in an infinite-dimensional setting. In addition to the reconstruction, we quantify the uncertainty of the predicted boundaries. Our approach is goal-oriented, meaning that we directly detect the discontinuities from the data instead of reconstructing the entire image. This drastically reduces the dimension of the problem, which makes the application of Markov Chain Monte Carlo (MCMC) methods feasible. We show that our method provides an excellent platform for challenging X-ray CT scenarios (e.g., in the case of noisy data, limited angle imaging, or sparse angle imaging). We investigate the performance and accuracy of our method on synthetic data as well as real-world data. The numerical results indicate that our method provides an accurate method for detecting boundaries of piecewise smooth regions and quantifies the uncertainty in the prediction.