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Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion

In: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author

Listed:
  • Florian Faucher

    (University of Vienna, Faculty of Mathematics
    Inria Bordeaux Sud-Ouest, Project-Team Makutu)

  • Clemens Kirisits

    (University of Vienna, Faculty of Mathematics)

  • Michael Quellmalz

    (Technical University Berlin, Institute of Mathematics)

  • Otmar Scherzer

    (University of Vienna, Faculty of Mathematics
    Johann Radon Institute for Computational and Applied Mathematics (RICAM)
    Christian Doppler Laboratory for Mathematical Modeling and Simulation of Next Generations of Ultrasound Devices (MaMSi))

  • Eric Setterqvist

    (Johann Radon Institute for Computational and Applied Mathematics (RICAM))

Abstract

In this chapter, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the scattered waves. Conventional DT relies on the Fourier diffraction theorem, which is applicable under the condition of weak scattering. However, if the object has high contrasts or is too large compared to the wavelength, it tends to produce multiple scattering, which complicates the reconstruction. In this chapter, we give a survey on diffraction tomography and compare the reconstruction of low- and high-contrast objects. We also implement and compare the reconstruction using the full waveform inversion method which, contrary to the Born and Rytov approximations, works with the total field and is more robust to multiple scattering.

Suggested Citation

  • Florian Faucher & Clemens Kirisits & Michael Quellmalz & Otmar Scherzer & Eric Setterqvist, 2023. "Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion," Springer Books, in: Ke Chen & Carola-Bibiane Schönlieb & Xue-Cheng Tai & Laurent Younes (ed.), Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, chapter 8, pages 273-312, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98661-2_115
    DOI: 10.1007/978-3-030-98661-2_115
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