A Phaseless Extended Rytov Approximation for Strongly Scattering Low-Loss Media and Its Application to Indoor Imaging

Abstract

Imaging objects with high relative permittivity and large electrical size remains a challenging problem in the field of inverse scattering. In this work, we present a phaseless inverse scattering method that can accurately reconstruct objects even with these attributes. The novelty of the approach is that it uses a high-frequency approximation for waves passing through lossy media to provide corrections to the conventional Rytov approximation (RA). We refer to this technique as the extended phaseless Rytov approximation for low-loss media (xPRA-LM). Simulation and experimental results are provided for RF indoor imaging using phaseless measurements acquired from 2.4-GHz-based WiFi nodes. We demonstrate that the approach provides accurate reconstruction of objects up to relative permittivities of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$15+1.5j$ </tex-math></inline-formula> for object sizes greater than 30 wavelengths. Even at higher relative permittivities of up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon _{r}=77+ 7j$ </tex-math></inline-formula> , object shape reconstruction remains accurate; however, the reconstruction amplitude is less accurate. To the best of our knowledge, xPRA-LM is the first linear phaseless inverse scattering approximation with such a large validity range and can be used to achieve the potential of RF and microwave imaging in applications such as indoor RF imaging.