Accurate Indoor Radio Frequency Imaging using a New Extended Rytov Approximation for Lossy Media

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 image and reconstruct objects even with these attributes. The reconstruction accuracy obtained under these conditions has not been achieved previously and can therefore open up the area to technologically important applications such as indoor Radio Frequency (RF) and microwave imaging. The novelty of the approach is that it utilizes 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 as well as experimental results are provided for indoor RF imaging using phaseless measurements from 2.4 GHz based WiFi nodes. We demonstrate that the approach provides accurate reconstruction of an object up to relative permittivities of $15+j1.5$ for object sizes greater than $20 \lambda$ ($\lambda$ is wavelength inside object). Even at higher relative permittivities of up to $\epsilon_r=77+j 7$, object shape reconstruction remains accurate, however the reconstruction amplitude is less accurate. These results have not been obtained before and can be utilized to achieve the potential of RF and microwave imaging in applications such as indoor RF imaging.