Domain-Factored Untrained Deep Prior for Spectrum Cartography

Spectrum cartography (SC) aims to estimate the radio power map of multiple emitters over space and frequency using limited sensor data. Recent advances leverage learned deep generative models (DGMs) as structural priors, achieving state-of-the-art performance by capturing complex spatial-spectral patterns. However, DGMs require large training datasets and may suffer under distribution shifts. To address these limitations, we propose a training-free SC approach based on untrained neural networks (UNNs), which encode structural priors through architectural design. Our custom UNN exploits a spatio-spectral factorization model rooted in the physical structure of radio maps, enabling low sample complexity. Experiments show that our method matches the performance of DGM-based SC without any training data.