  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.
