[Paper Review] Accurate Indoor Radio Frequency Imaging using a New Extended Rytov Approximation for Lossy Media

Amartansh Dubey, Samruddhi Deshmukh+3 more|arXiv (Cornell University)|Oct 7, 2021

Microwave Imaging and Scattering Analysis42 references4 citations

TL;DR

This paper proposes an extended phaseless Rytov approximation (xPRA-LM) that corrects the conventional Rytov approximation for lossy, high-permittivity media, enabling accurate indoor RF imaging using only phaseless measurements from 2.4 GHz WiFi nodes. It achieves high-fidelity shape and permittivity reconstruction for objects up to 20λ in size with relative permittivity as high as 77+j7, significantly outperforming prior methods in both simulation and experiment.

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 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 $20 λ$ ($λ$ is wavelength inside object). Even at higher relative permittivities of up to $ε_r=77+j 7$, 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.

Motivation & Objective

• Address the lack of accurate, formal inverse scattering methods for large, high-permittivity scatterers in lossy media.
• Overcome limitations of existing linear and nonlinear techniques that fail for εr > 3 and electrical sizes > λ₀.
• Enable practical indoor RF imaging using only phaseless measurements, avoiding the need for signal synchronization.
• Achieve accurate reconstruction of both shape and the imaginary part of the contrast function (related to loss and permittivity) for complex media.
• Demonstrate the method's validity and accuracy in real-world indoor environments using 2.4 GHz WiFi nodes.

Proposed method

• Derive corrections to the conventional Rytov approximation by incorporating a high-frequency approximation for waves in lossy media.
• Formulate the Extended Phaseless Rytov Approximation for Low Loss Media (xPRA-LM) to model wave propagation through lossy, high-permittivity scatterers.
• Use phaseless measurements (RSSI) from 2.4 GHz WiFi nodes as input, eliminating the need for phase synchronization.
• Model the scattered field using a high-order ray expansion, where the first-order ray dominates and higher-order rays are treated as small perturbations.
• Apply logarithmic transformation to the complex amplitude ratio to extract phase information, approximating the scattered field as dominated by the first-order ray.
• Reconstruct the contrast function by combining the real and imaginary parts, with particular emphasis on accurate estimation of the imaginary component for material identification.

Experimental results

Research questions

• RQ1 Can a phaseless inverse scattering method accurately reconstruct objects with relative permittivity up to 77+j7 and electrical size exceeding 20λ?
• RQ2 Does the xPRA-LM method provide improved accuracy over conventional Rytov approximation in lossy, high-permittivity media?
• RQ3 Can accurate shape and permittivity reconstruction be achieved using only phaseless RSSI measurements from commercial WiFi nodes in real indoor environments?
• RQ4 Why do conventional methods fail to reconstruct the real part of the contrast function for strong scatterers, and can the imaginary part be used effectively for material identification?
• RQ5 What is the theoretical and practical validity range of the extended Rytov approximation for lossy media in practical imaging scenarios?

Key findings

• The xPRA-LM method achieves accurate shape reconstruction for objects with relative permittivity up to 15+j1.5 and electrical size greater than 20λ.
• For higher permittivities up to 77+j7, shape reconstruction remains accurate, though amplitude reconstruction is less precise.
• The method provides accurate estimation of the imaginary part of the contrast function, enabling material identification even for strong scatterers.
• Reconstruction of the real part of the contrast function is poor for strong scatterers (e.g., PSNR < 10 dB, SSIM < 0.8), confirming the limitations of conventional RA.
• The method outperforms existing phaseless techniques in both simulation and experimental indoor RF imaging using 2.4 GHz WiFi nodes.
• Theoretical analysis confirms that higher-order rays contribute negligibly to the scattered field, validating the dominance of the first-order ray in the xPRA-LM model.