Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion

Florian Faucher (), Clemens Kirisits (), Michael Quellmalz (), Otmar Scherzer () and Eric Setterqvist ()
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Florian Faucher: University of Vienna, Faculty of Mathematics
Clemens Kirisits: University of Vienna, Faculty of Mathematics
Michael Quellmalz: Technical University Berlin, Institute of Mathematics
Otmar Scherzer: University of Vienna, Faculty of Mathematics
Eric Setterqvist: Johann Radon Institute for Computational and Applied Mathematics (RICAM)

Chapter 8 in Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, 2023, pp 273-312 from Springer

Abstract: 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.

Keywords: Diffraction tomography; Mathematical imaging; Fourier diffraction theorem; Full waveform inversion; Born approximation; Rytov approximation; Inverse problems (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-98661-2_115

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DOI: 10.1007/978-3-030-98661-2_115

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