Robust artefact reduction in tomography using Student’s t data fitting

Algebraic methods are popular for tomographic image reconstruction from limited data. These methods typically minimize the Euclidean norm of the residual of the corresponding linear equation system. The underlying assumption of this approach is that the noise has a Gaussian distribution. However, in cases where large outliers are present in the projection data, e.g., due to defective camera pixels, photon starvation from metal implants etc., the equation system is not consistent and the reconstruction will be fitted to these outliers, resulting in artefacts in the reconstruction. In this paper we use a penalty function for the residual that is based on the maximum likelihood estimate from the Student’s t distribution, which assigns a smaller penalty to outliers. No preprocessing is required to locate the outliers. We demonstrate the effectiveness of this approach on a 3D cone-beam simulated dataset for a series of perturbations in the projection data. Our results suggest that artefacts due to metal objects, defective camera pixels, or corrupted (randomized) projection images can be suppressed by using algebraic reconstruction methods in combination with the Student’s t penalty function.