Computed Tomography Reconstruction with Uncertain View Angles by Iteratively Updated Model Discrepancy

We propose a new model and a corresponding iterative algorithm for Computed Tomography (CT) when the view angles are uncertain. The uncertainty is described by an additive model discrepancy term which is included in the data fidelity term of a total variation regularized variational model. We approximate the model discrepancy with a Gaussian distribution. Our iterative algorithm alternates between updating the CT reconstruction and parameters of the model discrepancy. By assuming that the uncertainties in the view angles are independent we achieve a covariance matrix structure that we can take advantage of in a stochastic primal dual method to greatly reduce the computational work compared to classical primal dual methods. Using simulations with 2D problems we demonstrate that our method is able to reduce the reconstruction error and improve the visual quality, compared to methods that ignore the uncertainties in the angles.