Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion

Abstract

In this paper, 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. 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.

arXiv comment32 pages, 21 figures

References in corpus (4)

• Adjoint-state method for Hybridizable Discontinuous Galerkin discretization, application to the inverse acoustic wave problem
• Full Reciprocity-Gap Waveform Inversion in the frequency domain, enabling sparse-source acquisition
• An SVD in Spherical Surface Wave Tomography
• Reciprocity-gap misfit functional for Distributed Acoustic Sensing, combining data from passive and active sources

Cited by in corpus (3)

• Motion Detection in Diffraction Tomography by Common Circle Methods
• Generalized Fourier Diffraction Theorem and Filtered Backpropagation for Tomographic Reconstruction
• Slicing of Radial Functions: a Dimension Walk in the Fourier Space