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

Abstract

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

Registration-based multi-orientation tomography

“…The PWLS approach should lead to a better solution, giving a lower weight to the measurements with low intensity and, supposedly, high error. The Student's-T approach [29] should lead to a comparable result as it makes outliers less significant.…”

“…To make sure that the measurements with high error magnitude are penalized, we will consider two minimization approaches: the so called Penalized Weighted Least Squares (PWLS) [28] and an approach based on Student's-t penalty (SP) [29]. The PWLS approach can be expressed as a minimization problem of the following form:…”

“…where summation is carried out for all elements of the residual x;σ is an error variance parameter which is estimated in [29] using the following linear search:…”

“…Fig. 4, one can see a comparison of the standard FDK approach [43], and the FDK-based fusion approach that was recently described in [21] and three algebraic algorithms: Simultaneous Iterative Reconstruction Technique (SIRT), Penalized Weighed Least Squares (PWLS) and an algorithm based on Student's-T distribution (see [29]). Axis of rotation of the additional data used in each reconstruction is indicated by a white arrow (axis of rotation) and a yellow circle (orbit of rotation).…”

Model-based iterative reconstruction using higher-order regularization of dynamic synchrotron data

“…It has been shown in [20,21] that a specific form of the Huber misfit can be used to compensate for consistent offsets in data:…”