{"ID":2867176,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.19056","arxiv_id":"2509.19056","title":"Bayesian Convolutional Neural Networks for Prior Learning in Graph Signal Recovery","abstract":"Graph signal recovery (GSR) is a fundamental problem in graph signal processing, where the goal is to reconstruct a complete signal defined over a graph from a subset of noisy or missing observations. A central challenge in GSR is that the underlying statistical model of the graph signal is often unknown or too complex to specify analytically. To address this, we propose a flexible, data-driven framework that learns the signal prior directly from training samples. We develop a Bayesian convolutional neural network (BCNN) architecture that models the prior distribution of graph signals using graph-aware filters based on Chebyshev polynomials. By interpreting the hidden layers of the CNN as Gibbs distributions and employing Gaussian mixture model (GMM) nonlinearities, we obtain a closed-form and expressive prior. This prior is integrated into a variational Bayesian (VB) inference framework to estimate the posterior distribution of the signal and noise precision. Extensive experiments on synthetic and real-world graph datasets demonstrate that the proposed BCNN-GSR algorithm achieves accurate and robust recovery across a variety of signal distributions. The method generalizes well to complex, non-Gaussian signal models and remains computationally efficient, making it suitable for practical large-scale graph recovery tasks.","short_abstract":"Graph signal recovery (GSR) is a fundamental problem in graph signal processing, where the goal is to reconstruct a complete signal defined over a graph from a subset of noisy or missing observations. A central challenge in GSR is that the underlying statistical model of the graph signal is often unknown or too complex...","url_abs":"https://arxiv.org/abs/2509.19056","url_pdf":"https://arxiv.org/pdf/2509.19056v1","authors":"[\"Razieh Torkamani\",\"Arash Amini\",\"Hadi Zayyani\",\"Mehdi Korki\"]","published":"2025-09-23T14:21:03Z","proceeding":"eess.SP","tasks":"[\"eess.SP\"]","methods":"[\"Convolutional Neural Network\"]","has_code":false}