A Novel Tomographic Reconstruction Method Based on the Robust Student's t Function For Suppressing Data Outliers

Regularized iterative reconstruction methods in computed tomography can be effective when reconstructing from mildly inaccurate undersampled measurements. These approaches will fail, however, when more prominent dataerrors, or outliers, are present. These outliers are associated with various inaccuracies of the acquisition process: defective pixels or miscalibrated camerasensors, scattering, missing angles, etc. To account for such large outliers, robust data misfit functions, such as the generalized Huber function, have beenapplied successfully in the past. In conjunction with regularization techniques, these methods can overcome problems with both limited data and outliers. Thispaper proposes a novel reconstruction approach using a robust data fitting term which is based on the Student’s t distribution. This misfit promises to beeven more robust than the Huber misfit as it assigns a smaller penalty to large outliers. We include the total variation regularization term and automaticestimation of a scaling parameter that appears in the Student’s t function. We demonstrate the effectiveness of the technique by using a realistic synthetic phantom and also apply it to a real neutron dataset.