Abstract
Movements of the object during the data collection in computerized tomography can introduce motion artefacts in the reconstructed image. They can be reduced by employing information about the dynamic behaviour within the reconstruction step. However, inaccuracies concerning the movement are inevitable in practice. In this article, we give an explicit characterization of what is visible in an image obtained by a reconstruction algorithm with incorrect motion information. Then, we use this result to study in detail the situation of locally deforming objects, i.e. individual parts of the object have a different dynamic behaviour. In this context, we prove that additional artefacts arise due to the global nature of the Radon transform, even if the motion is exactly known. Based on our analysis, we propose a numerical scheme to reduce these artefacts in the reconstructed image. All our results are illustrated by numerical examples.
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