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Artifacts and Visible Singularities in Limited Data X-Ray Tomography

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Abstract

We describe a principle to determine which features of an object will be easy to reconstruct from limited X-ray CT data and which will be difficult. The principle depends on the geometry of the data set, and it applies to any limited data set. We also describe a characterization of Frikel and the author explaining artifacts that can be added to limited angle reconstructions, and we provide an easy-to-implement method to decrease them. These ideas are justified using microlocal analysis, deep mathematics that involves Fourier theory. Reconstructions from simulated and real limited data are given to illustrate our ideas.

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Acknowledgements

The author is indebted to DTU Compute for a stimulating and congenial semester. He thanks his DTU colleagues, graduate students, and Danish high school students with whom he discussed these ideas for their astute questions and observations about this work. The author thanks Jürgen Frikel for discussions and work that informed this article as well as for Fig. 8. He thanks Leise Borg and Jakob Jørgensen for their insights on limited data tomography. The author also thanks Ming Jiang for helpful discussions about this research. He thanks the local organizers for a stimulating International Conference on Sensing and Imaging, 2016 in Taiyuan, China. The author thanks the U.S. National Science Foundation for support under Grant DMS 1311558 and the Otto Mønsteds Fond for its support during his time at Danish Technical University.

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  1. Eric Todd Quinto

    Present address: DTU Compute, Danish Technical University, Kongens Lyngby, Denmark

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  1. Department of Mathematics, Tufts University, Medford, MA, USA

    Eric Todd Quinto

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Correspondence to Eric Todd Quinto.

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

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Quinto, E.T. Artifacts and Visible Singularities in Limited Data X-Ray Tomography. Sens Imaging 18, 9 (2017). https://doi.org/10.1007/s11220-017-0158-7

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