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.
Highlights
T OMOGRAPHIC imaging provides an opportunity to explore the inner structure of materials in a non-destructive fashion using penetrating electromagnetic radiation (X-rays) or particle radiation [1]
When the measurements are densely sampled over a full angular range of π radians and not noisy, one can recover the attenuation coefficients using direct reconstruction methods such as Filtered Back Projection (FBP) [3]
We investigate the use of various robust data misfit penalties in conjunction with the Total Variation (TV) penalty to minimize artifacts
Summary
T OMOGRAPHIC imaging provides an opportunity to explore the inner structure of materials in a non-destructive fashion using penetrating electromagnetic radiation (X-rays) or particle radiation (neutrons) [1]. The image reconstruction problem entails recovering the unknown attenuation coefficients xj from the intensity measurements bi. When the measurements are densely sampled over a full angular range of π radians and not noisy, one can recover the attenuation coefficients using direct reconstruction methods such as Filtered Back Projection (FBP) [3]. No matter how successful the preprocessing approach is, it includes modification (filtration) of measurements This can often result in a biased reconstructed image with introduced artifacts due to the filtering process [12]. In this case, the use of IIR is not recommended since the data have been modified unpredictably and do not represent real measurements.
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