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 data errors, or outliers,
are present. These outliers are associated with various inaccuracies
of the acquisition process: defective pixels or miscalibrated camera
sensors, scattering, missing angles, etc. To account for such
large outliers, robust data misfit functions, such as the generalized
Huber function, have been applied successfully in the past.
In conjunction with regularization techniques, these methods can
overcome problems with both limited data and outliers. This paper
proposes a novel reconstruction approach using a robust data fitting
term which is based on the Student’s t distribution. This misfit
promises to be even more robust than the Huber misfit as it assigns
a smaller penalty to large outliers. We include the total variation
regularization term and automatic estimation 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.