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.

当视角不确定时，我们为计算机断层扫描（CT）提出了一种新的模型和一种相应的迭代算法。不确定性由加法模型差异项描述，该变量包括在总变化正则化变异模型的数据保真度术语中。我们用高斯分布近似模型差异。我们的迭代算法在更新CT重建和模型差异参数之间交替。通过假设视角的不确定性是独立的，我们获得了协方差矩阵结构，与经典的原始对偶方法相比，我们可以在随机原始对偶方法中利用该协方差矩阵结构来大大减少计算量。