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Iterative Region-of-Interest Reconstruction from Limited Data Using Prior Information

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Abstract

In practice, computed tomography and computed laminography applications suffer from incomplete data. In particular, when inspecting large objects with extremely different diameters in longitudinal and transversal directions or when high resolution reconstructions are desired, the physical conditions of the scanning system lead to restricted data and truncated projections, also known as the interior or region-of-interest (ROI) problem. To recover the searched-for density function of the inspected object, we derive a semi-discrete model of the ROI problem that inherently allows the incorporation of geometrical prior information in an abstract Hilbert space setting for bounded linear operators. Assuming that the attenuation inside the object is approximately constant, as for fibre reinforced plastics parts or homogeneous objects where one is interested in locating defects like cracks or porosities, we apply the semi-discrete Landweber–Kaczmarz method to recover the inner structure of the object inside the ROI from the measured data resulting in a semi-discrete iteration method. Finally, numerical experiments for three-dimensional tomographic applications with both an inherent restricted source and ROI problem are provided to verify the proposed method for the ROI reconstruction.

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Acknowledgements

The work of the authors was partially supported by Deutsche Forschungsgemeinschaft (DFG) under Grant LO 310/13-1, by the Sino-German Center for Research Promotion (SGC) under Grant GZ 1025 and the Bundesministerium für Bildung und Forschung (BMBF) project IPro (#20H1309B).

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Authors and Affiliations

  1. Department of Mathematics, Saarland University, Campus E1.1, 66123, Saarbrücken, Germany

    Jonas Vogelgesang

  2. Fraunhofer Institute for Nondestructive Testing (IZFP), Campus E3.1, 66123, Saarbrücken, Germany

    Christian Schorr

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  1. Jonas Vogelgesang
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  2. Christian Schorr
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Correspondence to Jonas Vogelgesang.

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This article is part of the Topical Collection on Recent Developments in Sensing and Imaging.

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Vogelgesang, J., Schorr, C. Iterative Region-of-Interest Reconstruction from Limited Data Using Prior Information. Sens Imaging 18, 16 (2017). https://doi.org/10.1007/s11220-017-0165-8

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  • DOI: https://doi.org/10.1007/s11220-017-0165-8

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