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An algorithm for total variation regularized photoacoustic imaging

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Abstract

Recovery of image data from photoacoustic measurements asks for the inversion of the spherical mean value operator. In contrast to direct inversion methods for specific geometries, we consider a semismooth Newton scheme to solve a total variation regularized least squares problem. During the iteration, each matrix vector multiplication is realized in an efficient way using a recently proposed spectral discretization of the spherical mean value operator. All theoretical results are illustrated by numerical experiments.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Copenhagen, Denmark

    Yiqiu Dong

  2. Institute of Mathematics, University Osnabrück, Osnabrück, Germany

    Torsten Görner & Stefan Kunis

  3. Institute of Computational Biology, Helmholtz Zentrum München, München, Germany

    Stefan Kunis

Authors
  1. Yiqiu Dong
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  2. Torsten Görner
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  3. Stefan Kunis
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Correspondence to Stefan Kunis.

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Communicated by: Leslie Greengard

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Dong, Y., Görner, T. & Kunis, S. An algorithm for total variation regularized photoacoustic imaging. Adv Comput Math 41, 423–438 (2015). https://doi.org/10.1007/s10444-014-9364-1

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  • DOI: https://doi.org/10.1007/s10444-014-9364-1

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