The One-Dimensional Inverse Problem in Photoacoustics. Numerical Testing

  • D. LangemannEmail author
  • A. S. Mikhaylov
  • V. S. Mikhaylov

The problem of reconstruction of the Cauchy data for the wave equation in ℝ1 from the measurements of its solution on the boundary of a finite interval is considered. This is a one-dimensional model for the multidimensional problem of photoacoustics, which was studied previously. The method was adapted and simplified for the one-dimensional situation. The results of numerical testing to see the rate of convergence and the stability of the procedure are given. Some hints are also given on how the procedure of reconstruction can be simplified in the 2d and 3d cases.


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  1. 1.
    S. A. Avdonin and S. A. Ivanov, Families of Exponentials, Cambridge University Press, Cambridge (1995).zbMATHGoogle Scholar
  2. 2.
    M. I. Belishev, D. Langemann, A. S. Mikhaylov, and V. S. Mikhaylov, “On an inverse problem in photoacoustics,” J. Inverse and Ill-posed Problems (2018).Google Scholar
  3. 3.
    Minghua Xua and Lihong V. Wang, “Photoacoustic imaging in biomedicine,” Review Sci. Instruments, No. 4, 77.Google Scholar
  4. 4.
    P. Kuchment and L. Kunyansky, “Mathematics of thermoacoustic and photoacoustic tomography,” in: Handbook of Mathematical Methods in Imaging, Vol. 2 (2010), pp. 817–866.CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • D. Langemann
    • 1
    Email author
  • A. S. Mikhaylov
    • 2
  • V. S. Mikhaylov
    • 2
  1. 1.Technische Universität Braunschweig, Inst. Computational Mathematics, AG PDEBraunschweigGermany
  2. 2.St. Petersburg Department of the V. A. Steklov Institute of Mathematicsthe Russian Academy of Sciences, St. Petersburg State UniversitySt. PetersburgRussia

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