# Reconstruction of SINR Maps from Sparse Measurements using Group Equivariant Non-Expansive Operators

arXiv: https://arxiv.org/abs/2507.19349 · HTML: https://mlsanity.com/paper/2507.19349/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 83 references that are in the map.
- First posted on arXiv 25 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [RadioUNet: Fast Radio Map Estimation with Convolutional Neural Networks](https://mlsanity.com/paper/1911.09002/) (2019)
- [On the Road to 6G: Visions, Requirements, Key Technologies and Testbeds](https://mlsanity.com/paper/2302.14536/) (2023)
- [Sionna RT: Differentiable Ray Tracing for Radio Propagation Modeling](https://mlsanity.com/paper/2303.11103/) (2023)
- [Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning](https://mlsanity.com/paper/1812.11832/) (2018)
- [Combining persistent homology and invariance groups for shape comparison](https://mlsanity.com/paper/1312.7219/) (2013)
- [Generalized Permutants and Graph GENEOs](https://mlsanity.com/paper/2206.14798/) (2022)
- [Mathematical Foundation of Interpretable Equivariant Surrogate Models](https://mlsanity.com/paper/2503.01942/) (2025)
- [GENEOnet: A new machine learning paradigm based on Group Equivariant Non-Expansive Operators. An application to protein pocket detection](https://mlsanity.com/paper/2202.00451/) (2022)
- [A novel approach to graph distinction through GENEOs and permutants](https://mlsanity.com/paper/2406.08045/) (2024)
- [Towards Addressing Training Data Scarcity Challenge in Emerging Radio Access Networks: A Survey and Framework](https://mlsanity.com/paper/2304.12480/) (2023)
- [Self-Learning for Received Signal Strength Map Reconstruction with Neural Architecture Search](https://mlsanity.com/paper/2105.07768/) (2021)

## Abstract (arXiv)

As sixth generation (6G) wireless networks evolve, accurate signal-to-interference-noise ratio (SINR) maps are becoming increasingly critical for effective resource management and optimization. However, acquiring such maps at high resolution is often cost-prohibitive, creating a severe data scarcity challenge. This necessitates machine learning (ML) approaches capable of robustly reconstructing the full map from extremely sparse measurements. To address this, we introduce a novel reconstruction framework based on Group Equivariant Non-Expansive Operators (GENEOs). Unlike data-hungry ML models, GENEOs are low-complexity operators that embed domain-specific geometric priors, such as translation invariance and rotational equivariance, directly into their structure. This provides a strong inductive bias, enabling effective reconstruction from very few samples. Our key insight is that for network management, preserving the topological structure of the SINR map, such as the geometry of coverage holes and interference patterns, is often more critical than minimizing pixel-wise error. We validate our approach on realistic ray-tracing-based urban scenarios, evaluating performance with both statistical metrics (mean squared error (MSE)) and, crucially, a topological metric (1-Wasserstein distance). Results show that our method achieves superior statistical and topological accuracy across diverse urban scenarios. Compared to the best-performing baselines, GENEO reduces MSE up to 45% and decreases the 1-Wasserstein distance up to 54%. Crucially, these performance gains are maintained even under the most extreme tested conditions, such as a 1% sampling rate with a 30% measurement error, and when measurements are spatially biased. This demonstrates the practical advantage of GENEOs for creating structurally accurate SINR maps that are more reliable for downstream network optimization tasks.