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.

Total variation-based reconstruction and phase retrieval for diffraction tomography

“…Equation ( 17) is a linear equation system that may be solved in the least-square sense by applying the iterative conjugate gradient (CG) method. This approach has been successfully applied in ODT [25,45] as well as in X-ray imaging [58], magnetic resonance imaging [48], or spherical tomography [38]. We consider the overdetermined case M N d´1 ě K d .…”