RINN: One Sample Radio Frequency Imaging based on Physics Informed Neural Network

TL;DR

RINN introduces a physics-informed neural network for RF imaging from a single phaseless sample, embedding Maxwell-based constraints to enable electromagnetic inverse scattering without large labeled datasets. By employing two implicit neural representations (for complex permittivity and induced current) and physics-based loss terms, it achieves robust imaging on phaseless data and competitive results against phase-based methods. The approach demonstrates strong performance on Estonia Austria and MNIST targets, with RRMSE around 0.08 on phase data and 0.11 on phaseless data, and shows resilience to moderate noise, enabling potential deployment on ubiquitous RF devices such as Wi-Fi. This work broadens the practicality of RF imaging by reducing data requirements and leveraging existing RF infrastructure for non-line-of-sight sensing in multimodal contexts.

Abstract

Due to its ability to work in non-line-of-sight and low-light environments, radio frequency (RF) imaging technology is expected to bring new possibilities for embodied intelligence and multimodal sensing. However, widely used RF devices (such as Wi-Fi) often struggle to provide high-precision electromagnetic measurements and large-scale datasets, hindering the application of RF imaging technology. In this paper, we combine the ideas of PINN to design the RINN network, using physical constraints instead of true value comparison constraints and adapting it with the characteristics of ubiquitous RF signals, allowing the RINN network to achieve RF imaging using only one sample without phase and with amplitude noise. Our numerical evaluation results show that compared with 5 classic algorithms based on phase data for imaging results, RINN's imaging results based on phaseless data are good, with indicators such as RRMSE (0.11) performing similarly well. RINN provides new possibilities for the universal development of radio frequency imaging technology.

Figures (5)

• Figure 1: The incident wave $\bm{E}_i$ induces a sensing current $\bm{J}$ in the dielectric medium, thereby exciting scattered waves $\bm{E}_s$. The variation in permittivity among different media provides an opportunity for imaging utilizing these scattered waves.
• Figure 2: The amplitude of WiFi signals is more stable than the phase after smoothing.
• Figure 3: RINN. We use the idea of PINN to design a neural network RINN for imaging based on one sample using phaseless data. The main idea is to obtain a set of solutions that satisfy the constraints of Maxwell's equations (Equ. \ref{['eq:model-d']}) with the help of the encoding capability of MLP networks. The uniqueness of the solution to the electromagnetic inverse scattering problem has been proven. We sample from a multidimensional Gaussian distribution to obtain $\bm{X}$, then encode it using $\varepsilon$-MLP to obtain the distribution of complex permittivity; noting that sensing current $\bm{J}$ is a function of incident waves and spatial coordinates, we embed incident waves into $\bm{X}$ and then encode them using $\bm{J}$-MLP network to obtain an estimate $\bm{J}$ for sensing current. Equ. \ref{['eq:model-d']} has two constraints: one is that received signals should be as close as possible to actual values, and another is that two representation schemes for $\bm{J}$ are equivalent (outputs from J-MLP and results from Equ. \ref{['eq:current-d']}). Based on this we designed loss functions $\mathcal{L}_{sa}$ and $\mathcal{L}_\mathcal{D}$. Then through multiple rounds training until convergence was achieved by our network.
• Figure 4: The imaging results of RINN. We used Austrian patterns and handwritten images from the MNIST dataset as imaging targets, setting them to different permittivities, and then obtained scattering signals using the method of moments simulation. The top row of images shows the ground truth of the targets, while the bottom row shows the imaging results obtained by the RINN network based on phaseless data. The permittivity for the first three columns on the left is set to 1.6, for the fourth column it is set to a smaller value of 1.1, and for the rightmost column it is set to a larger value of 1.8.
• Figure 5: The processing results of the RINN network for noisy data. We use Austrian patterns as targets, then add different levels of noise to the amplitude of the received signals, and perform imaging using the RINN network. The results show that for lower levels of noise, the RINN imaging results are good; for higher levels of noise, although distorted, the basic pattern can still be discerned. This has potential to leverage the ubiquitous nature of RF signals in applications such as multimodal sensing.