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An algorithm for total variation regularized photoacoustic imaging

Advances in Computational Mathematics volume 41, pages 423–438 (2015)Cite this article

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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Author information

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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Corresponding author

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

Keywords

  • Spherical mean operator
  • Fast Fourier transform
  • Total variation regularization
  • Photoacoustic imaging

Mathematics Subject Classifications (2010)

  • 65T50
  • 44A12
  • 92C55