Bayesian Convolutional Neural Networks for Prior Learning in Graph Signal Recovery
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915509309538304 |
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| author | Torkamani, Razieh Amini, Arash Zayyani, Hadi Korki, Mehdi |
| author_facet | Torkamani, Razieh Amini, Arash Zayyani, Hadi Korki, Mehdi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19056 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bayesian Convolutional Neural Networks for Prior Learning in Graph Signal Recovery Torkamani, Razieh Amini, Arash Zayyani, Hadi Korki, Mehdi Signal Processing 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. |
| title | Bayesian Convolutional Neural Networks for Prior Learning in Graph Signal Recovery |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2509.19056 |