Node-Oriented Proactive Spectral Modulation: A Unified Fractional Framework for Graph Signal Denoising

Abstract: Graph signal denoising is a fundamental task in graph signal processing. While the node-oriented filtering approach enhances spatial adaptability, it suffers from spectral rigidity due to its reliance on the graph Fourier transform. Conversely, emerging fractional-domain transforms provide crucial spectral flexibility but are fundamentally limited by their globally shared filtering paradigm, failing to accommodate localized topological variations. To bridge this gap, this paper proposes a generalized node-oriented fractional filtering (NOFF) framework that seamlessly integrates localized spatial adaptability with proactive spectral modulation across various fractional transforms. However, straightforwardly assigning independent full-rank filters to all vertices incurs a prohibitive parameter space, leading to severe overfitting on random noise. To mitigate this, we introduce the low-rank NOFF (LRNOFF) architecture. By imposing a strict low-rank constraint, LRNOFF inherently acts as a powerful implicit regularizer, preventing noise memorization and ensuring the extraction of robust spectral bases. Furthermore, we develop an efficient computational implementation termed LRNOFF-Fast, which drastically reduces computational and memory overhead while preserving theoretical optimality. Experiments on real-world datasets demonstrate that the proposed framework achieves state-of-the-art performance.