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GLIP: Electromagnetic Field Exposure Map Completion by Deep Generative Networks

Mohammed Mallik, Davy P. Gaillot, Laurent Clavier

TL;DR

This work tackles urban RF-EMF exposure map completion under sparse sensing by proposing GLIP, a GAN-free method that leverages a Local Image Prior derived from observed data. GLIP uses a generator-based encoder-decoder (inspired by U-Net) to produce exposure maps $\\gamma = f(\\theta|Z_p)$ by minimizing $E(\\gamma, \\gamma_i) = ||(\\gamma - \\gamma_i) \\odot m||^2$ with ADAM, relying only on sparse measurements and avoiding large training datasets or simulated full maps. Evaluations over a $1 \,\\text{km}^2$ Lille region show that GLIP achieves high-fidelity reconstructions even with as few as 40–100 sensors, outperforming a GRIP baseline and reducing dependence on expensive simulators. The results indicate GLIP’s practical potential for fast, scalable urban RF-EMF exposure mapping under realistic sensing constraints, with future work aiming to enhance loss functions, add residual components, and extend to broader frequency/time dimensions.

Abstract

In Spectrum cartography (SC), the generation of exposure maps for radio frequency electromagnetic fields (RF-EMF) spans dimensions of frequency, space, and time, which relies on a sparse collection of sensor data, posing a challenging ill-posed inverse problem. Cartography methods based on models integrate designed priors, such as sparsity and low-rank structures, to refine the solution of this inverse problem. In our previous work, EMF exposure map reconstruction was achieved by Generative Adversarial Networks (GANs) where physical laws or structural constraints were employed as a prior, but they require a large amount of labeled data or simulated full maps for training to produce efficient results. In this paper, we present a method to reconstruct EMF exposure maps using only the generator network in GANs which does not require explicit training, thus overcoming the limitations of GANs, such as using reference full exposure maps. This approach uses a prior from sensor data as Local Image Prior (LIP) captured by deep convolutional generative networks independent of learning the network parameters from images in an urban environment. Experimental results show that, even when only sparse sensor data are available, our method can produce accurate estimates.

GLIP: Electromagnetic Field Exposure Map Completion by Deep Generative Networks

TL;DR

This work tackles urban RF-EMF exposure map completion under sparse sensing by proposing GLIP, a GAN-free method that leverages a Local Image Prior derived from observed data. GLIP uses a generator-based encoder-decoder (inspired by U-Net) to produce exposure maps by minimizing with ADAM, relying only on sparse measurements and avoiding large training datasets or simulated full maps. Evaluations over a Lille region show that GLIP achieves high-fidelity reconstructions even with as few as 40–100 sensors, outperforming a GRIP baseline and reducing dependence on expensive simulators. The results indicate GLIP’s practical potential for fast, scalable urban RF-EMF exposure mapping under realistic sensing constraints, with future work aiming to enhance loss functions, add residual components, and extend to broader frequency/time dimensions.

Abstract

In Spectrum cartography (SC), the generation of exposure maps for radio frequency electromagnetic fields (RF-EMF) spans dimensions of frequency, space, and time, which relies on a sparse collection of sensor data, posing a challenging ill-posed inverse problem. Cartography methods based on models integrate designed priors, such as sparsity and low-rank structures, to refine the solution of this inverse problem. In our previous work, EMF exposure map reconstruction was achieved by Generative Adversarial Networks (GANs) where physical laws or structural constraints were employed as a prior, but they require a large amount of labeled data or simulated full maps for training to produce efficient results. In this paper, we present a method to reconstruct EMF exposure maps using only the generator network in GANs which does not require explicit training, thus overcoming the limitations of GANs, such as using reference full exposure maps. This approach uses a prior from sensor data as Local Image Prior (LIP) captured by deep convolutional generative networks independent of learning the network parameters from images in an urban environment. Experimental results show that, even when only sparse sensor data are available, our method can produce accurate estimates.
Paper Structure (12 sections, 6 equations, 5 figures, 3 tables)

This paper contains 12 sections, 6 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Inverse problem formulation
  4. Exposure Reconstruction by Deep Learning
  5. Generator Architecture
  6. Results
  7. Evaluation protocol
  8. Evaluation metrics
  9. Implementation Details and Dataset
  10. Visual Analysis
  11. Quantitative Analysis and Impact of Sensor Density
  12. Conclusion

Figures (5)

  • Figure 1: The exposure reconstruction GLIP process. $Z_p$ is the input of the network. $\theta$ is the set of parameters and $\gamma_0$ the initial output of the network. $\gamma$ and $m$ are the reconstructed and mask images. $E$ is the loss function corresponding to each features. $f$ is the network function.
  • Figure 2: Proposed GLIP Generator Network
  • Figure 3: Visualization of the region of interest. a) showcases the experimental 1$km^2$ area, where red and blue represent sensors and transmitter respectively. b) reveals the city topology extracted as a raster from OpenStreetMap.
  • Figure 4: Visualization of the LIP a) LIP - 100 sensors , b) LIP - 60 sensors
  • Figure 5: Experimental results for GLIP: 1st row: Reference map from Veneris, 2nd row (Left to right): reconstructed maps for 20, 40, 60 and 100 sensors, 3rd row (Left to right): corresponding error maps.