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Nonlinear Compressed Sensing for Multi-emitter X-Ray Imaging

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Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10746))

Abstract

Compressed sensing is a powerful mathematical modelling tool to recover sparse signals from undersampled measurements in many applications, including medical imaging. A large body of work investigates the case with linear measurements, while compressed sensing with nonlinear measurements has been considered more recently. We continue this line of investigation by considering a novel type of nonlinearity with special structure that occurs in data acquired by multi-emitter X-ray tomosynthesis systems with spatio-temporal overlap. In [15] we proposed a nonlinear optimization model to deconvolve the overlapping measurements. In this paper we propose a model that exploits the structure of the nonlinearity and a nonlinear tomosynthesis algorithm that has a practical running time of solving only two linear subproblems at the equivalent resolution. We underpin and justify the algorithm by deriving RIP bounds for the linear subproblems and conclude with numerical experiments that validate the approach.

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Acknowledgments

We thank Adaptix Ltd for providing the X-ray measurements used in the experiments with real-world data. This work was supported by Adaptix Ltd and EPSRC EP/K503769/1, as well as by The Alan Turing Institute under the EPSRC grant EP/N510129/1.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK

    Maria Klodt & Raphael Hauser

Authors
  1. Maria Klodt
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  2. Raphael Hauser
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Corresponding author

Correspondence to Raphael Hauser .

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Editors and Affiliations

  1. Ca’ Foscari University of Venice, Venice, Italy

    Marcello Pelillo

  2. University of York, York, United Kingdom

    Edwin Hancock

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Klodt, M., Hauser, R. (2018). Nonlinear Compressed Sensing for Multi-emitter X-Ray Imaging. In: Pelillo, M., Hancock, E. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2017. Lecture Notes in Computer Science(), vol 10746. Springer, Cham. https://doi.org/10.1007/978-3-319-78199-0_13

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  • DOI: https://doi.org/10.1007/978-3-319-78199-0_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78198-3

  • Online ISBN: 978-3-319-78199-0

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