# Integrated Interpolation and Block-term Tensor Decomposition for Spectrum Map Construction

arXiv: https://arxiv.org/abs/2402.17138 · HTML: https://mlsanity.com/paper/2402.17138/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2024.

## Built on by (most cited first, 8 of 8)

- [Radio Map Estimation via Latent Domain Plug-and-Play Denoising](https://mlsanity.com/paper/2501.13472/) (2025)
- [Physics-Informed Neural Networks for MIMO Beam Map and Environment Reconstruction](https://mlsanity.com/paper/2510.21238/) (2025)
- [Self-Localizing MIMO Beam Mapping with Continuously Evolving Channel Memory](https://mlsanity.com/paper/2511.17007/) (2025)
- [ReVeal-MT: A Physics-Informed Neural Network for Multi-Transmitter Radio Environment Mapping](https://mlsanity.com/paper/2512.04100/) (2025)
- [RadioGen3D: 3D Radio Map Generation via Adversarial Learning on Large-Scale Synthetic Data](https://mlsanity.com/paper/2602.18744/) (2026)
- [CSI-tuples-based 3D Channel Fingerprints Construction Assisted by MultiModal Learning](https://mlsanity.com/paper/2603.25288/) (2026)
- [Statistical Channel Fingerprint Construction for Massive MIMO: A Unified Tensor Learning Framework](https://mlsanity.com/paper/2604.27574/) (2026)
- [Active Learning for Low-Altitude Radio Map Construction via Plug-and-Play Flow Matching](https://mlsanity.com/paper/2609.27486/) (2026)

## Abstract (arXiv)

This paper addresses the challenge of reconstructing a 3D power spectrum map from sparse, scattered, and incomplete spectrum measurements. It proposes an integrated approach combining interpolation and block-term tensor decomposition (BTD). This approach leverages an interpolation model with the BTD structure to exploit the spatial correlation of power spectrum maps. Additionally, nuclear norm regularization is incorporated to effectively capture the low-rank characteristics. To implement this approach, a novel algorithm that combines alternating regression with singular value thresholding is developed. Analytical justification for the enhancement provided by the BTD structure in interpolating power spectrum maps is provided, yielding several important theoretical insights. The analysis explores the impact of the spectrum on the error in the proposed method and compares it to conventional local polynomial interpolation. Extensive numerical results demonstrate that the proposed method outperforms state-of-the-art methods in terms of signal source separation and power spectrum map construction, and remains stable under off-grid measurements and inhomogeneous measurement topologies.