Generative Bayesian Spectrum Cartography: Unified Reconstruction and Active Sensing via Diffusion Models

2025-12-23

AI Summary

High-fidelity spectrum map reconstruction from sparse, non-uniform observations is an ill-posed inverse problem; existing approaches decouple reconstruction from sensing and lack theoretically grounded sampling mechanisms. This paper introduces the first integration of diffusion models into a Bayesian inverse framework to jointly enable spectrum reconstruction and active sensing. We propose an analytically tractable posterior diffusion transition kernel compatible with both linear and quantized measurement constraints, and pioneer a generative uncertainty-driven active sampling strategy. Our method unifies diffusion modeling, Bayesian inference, and conditional generation. It significantly improves reconstruction accuracy, sampling efficiency, and robustness under low-bit quantization, consistently outperforming interpolation, sparse optimization, and deep learning baselines across multiple quantitative metrics.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Active Learning
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

High-fidelity spectrum cartography is pivotal for spectrum management and wireless situational awareness, yet it remains a challenging ill-posed inverse problem due to the sparsity and irregularity of observations. Furthermore, existing approaches often decouple reconstruction from sensing, lacking a principled mechanism for informative sampling. To address these limitations, this paper proposes a unified diffusion-based Bayesian framework that jointly addresses spectrum reconstruction and active sensing. We formulate the reconstruction task as a conditional generation process driven by a learned diffusion prior. Specifically, we derive tractable, closed-form posterior transition kernels for the reverse diffusion process, which enforce consistency with both linear Gaussian and non-linear quantized measurements. Leveraging the intrinsic probabilistic nature of diffusion models, we further develop an uncertainty-aware active sampling strategy. This strategy quantifies reconstruction uncertainty to adaptively guide sensing agents toward the most informative locations, thereby maximizing spectral efficiency. Extensive experiments demonstrate that the proposed framework significantly outperforms state-of-the-art interpolation, sparsity-based, and deep learning baselines in terms of reconstruction accuracy, sampling efficiency, and robustness to low-bit quantization.

Problem

• Reconstructs high-fidelity spectrum maps from sparse, irregular observations
• Unifies reconstruction and active sensing in a Bayesian diffusion framework
• Develops uncertainty-aware sampling to maximize spectral efficiency adaptively

Innovation

• Unified diffusion-based Bayesian framework for spectrum reconstruction
• Closed-form posterior transition kernels for reverse diffusion process
• Uncertainty-aware active sampling strategy for adaptive sensing