arXiv subjects

Manjun Cui

Publications and source records attributed to Manjun Cui.

8 recordsLinked to original sources

arXiv2026

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

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.

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arXiv2026

A Unified Fractional Spectral Framework for Spatiotemporal Graph Signals: Bi-Fractional Transform and Geodesic Coupling

Graph signal processing extends spectral analysis to data supported on irregular domains. Existing fractional transforms for two-dimensional graph signals, including the two-dimensional graph fractional Fourier transform (GFRFT), typically impose a shared fractional order across dimensions, which limits adaptivity to heterogeneous spatiotemporal spectra. To address this limitation, we propose the two-dimensional graph bi-fractional Fourier transform, which assigns independent fractional orders to the factor graphs of a Cartesian product, enabling decoupled spectral control while preserving separability, unitarity, and invertibility. To further resolve the basis ambiguity in temporal fractional analysis, we develop a geodesic-coupled GFRFT by constructing a coupling path along the principal geodesic on the unitary manifold, thereby unifying graph-induced and discrete temporal bases with guaranteed unitarity and a closed-form inverse. Building on these transforms, we derive a differentiable Wiener-type filtering framework with a hybrid optimization strategy: the fractional orders are learned end-to-end from data, while the coupling parameter is fixed as a structural regularizer. Experiments on real-world time-varying graph datasets and dynamic image restoration tasks demonstrate consistent gains over state-of-the-art fractional transforms and competitive learning-based baselines.

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arXiv2026

FGFRFT: Fast Graph Fractional Fourier Transform via Exact Spectral Splitting and Fourier-Series Approximation

The graph fractional Fourier transform (GFRFT) for unitary graph Fourier transform (GFT) matrices can be interpreted through the scalar function $e^{j\alpha\theta}$ on the unit circle. Under the principal branch, its Fourier-series representation encounters an intrinsic obstruction at the spectral point $\lambda=-1$ for non-integer orders. To address this issue, we propose a fast graph fractional Fourier transform (FGFRFT) based on exact spectral splitting: the $\lambda=-1$ component is treated exactly, and the complementary component is approximated by a truncated Fourier series in integer powers of the GFT matrix. This construction yields an offline--online implementation that reduces the online complexity of repeated operator updates from $O(N^3)$ to $O(2LN^2)$ for truncation order $L$, while preserving differentiability with respect to the transform order. We further derive truncation-error bounds, approximate unitarity and additivity, and reconstruction-error bounds. Experiments on approximation accuracy, transform-order learning, image denoising, and point-cloud denoising show that FGFRFT provides substantial online acceleration while remaining close to the exact GFRFT under the tested settings.

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arXiv2025

Dynamic Multiple-Parameter Joint Time-Vertex Fractional Fourier Transform and its Intelligent Filtering Methods

Dynamic graph signal processing provides a principled framework for analyzing time-varying data defined on irregular graph domains. However, existing joint time-vertex transforms such as the joint time-vertex fractional Fourier transform assign only one fractional order to the spatial domain and another one to the temporal domain, thereby restricting their capacity to model the complex and continuously varying dynamics of graph signals. To address this limitation, we propose a novel dynamic multiple-parameter joint time-vertex fractional Fourier transform (DMPJFRFT) framework, which introduces time-varying fractional parameters to achieve adaptive spectral modeling of dynamic graph structures. By assigning distinct fractional orders to each time step, the proposed transform enables dynamic and flexible representation of spatio-temporal signal evolution in the joint time-vertex spectral domain. Theoretical properties of the DMPJFRFT are systematically analyzed, and two filtering approaches: a gradient descent-based method and a neural network-based method, are developed for dynamic signal restoration. Experimental results on dynamic graph and video datasets demonstrate that the proposed framework effectively captures temporal topology variations and achieves superior performance in denoising and deblurring tasks compared with some state-of-the-art graph-based transforms and neural networks.

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arXiv2025

MPFSR-Enhanced GNNs: Spectral Graph Neural Networks Enhancement Through Learnable Multiple-Parameter Graph Fractional Fourier Transforms

Graph neural networks (GNNs) excel in processing non-Euclidean data, but traditional spectral GNNs rely on static bases and fundamentally lack active spectral regulation. Although the graph fractional Fourier transform (GFRFT) introduces cross-domain modulation, it applies a uniform fractional parameter across all frequencies. This ignores frequency heterogeneity and restricts the models' adaptive capacity in graph node classification tasks. In the paper, we propose two novel types of multiple-parameter GFRFTs (MPGFRFTs) and establish their corresponding theoretical frameworks, including essential properties, computational complexity, and parameters differentiability. By assigning independent, learnable fractional parameters to distinct frequency bands, MPGFRFTs enable fine-grained spectral regulation. Then, we operationalize this mathematical framework by designing the adaptive multiple-parameter fractional spectral regulation (MPFSR) module, a plug-and-play component for mainstream spectral models. We also establish rigorous theoretical bounds on the spectral stability of this module, guaranteeing a stable and reliable convergence during the end-to-end parameters optimization. Experiments demonstrate that integrating the proposed MPFSR module alleviates the constraints of static bases and yields performance gains in node classification on complex graphs, advancing a novel paradigm for active spectral modulation in graph representation learning.

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arXiv2025

Graph Chirp Signal and Graph Fractional Vertex-Frequency Energy Distribution

Graph signal processing (GSP) has emerged as a powerful framework for analyzing data on irregular domains. In recent years, many classical techniques in signal processing (SP) have been successfully extended to GSP. Among them, chirp signals play a crucial role in various SP applications. However, graph chirp signals have not been formally defined despite their importance. Here, we define graph chirp signals and establish a comprehensive theoretical framework for their analysis. We propose the graph fractional vertex--frequency energy distribution (GFED), which provides a powerful tool for processing and analyzing graph chirp signals. We introduce the general fractional graph distribution (GFGD), a generalized vertex--frequency distribution, and the reduced interference GFED, which can suppress cross-term interference and enhance signal clarity. Furthermore, we propose a novel method for detecting graph signals through GFED domain filtering, facilitating robust detection and analysis of graph chirp signals in noisy environments. Moreover, this method can be applied to real-world data for denoising more effective than some state-of-the-arts, further demonstrating its practical significance.

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arXiv2024

Least-Squares Adaptive Filter-Based Cohen's Class Time-Frequency Distribution for Signal Denoising

Inspired by the use of adaptive kernel-based Cohen's class time-frequency distributions (CCTFDs) for cross-term suppression, this paper aims to explore novel adaptive kernel functions for denoising, with a particular focus on non-stationary signal processing in practical applications}. We integrate Wiener filter principle and the time-frequency filtering mechanism of CCTFD to design the least-squares adaptive filter method in the Wigner-Ville distribution (WVD) domain, giving birth to the least-squares adaptive filter-based CCTFD whose kernel function can be adjusted with the input signal automatically to achieve the minimum mean-square error denoising in the WVD domain. {Numerical experiments on typical simulated radar signals and real-world electrocardiogram data comprehensively demonstrate that the proposed adaptive CCTFD outperforms several state-of-the-art methods in noise suppression.

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arXiv2024

Convolution Type of Metaplectic Cohen's Distribution Time-Frequency Analysis Theory, Method and Technology

The conventional Cohen's distribution can't meet the requirement of additive noises jamming signals high-performance denoising under the condition of low signal-to-noise ratio, it is necessary to integrate the metaplectic transform for non-stationary signal fractional domain time-frequency analysis. In this paper, we blend time-frequency operators and coordinate operator fractionizations to formulate the definition of the metaplectic Wigner distribution, based on which we integrate the generalized metaplectic convolution to address the unified representation issue of the convolution type of metaplectic Cohen's distribution (CMCD), whose special cases and essential properties are also derived. We blend Wiener filter principle and fractional domain filter mechanism of the metaplectic transform to design the least-squares adaptive filter method in the metaplectic Wigner distribution domain, giving birth to the least-squares adaptive filter-based CMCD whose kernel function can be adjusted with the input signal automatically to achieve the minimum mean-square error (MSE) denoising in Wigner distribution domain. We discuss the optimal symplectic matrices selection strategy of the proposed adaptive CMCD through the minimum MSE minimization modeling and solving. Some examples are also carried out to demonstrate that the proposed filtering method outperforms some state-of-the-arts including Wiener filter and fixed kernel functions-based or adaptive Cohen's distribution in noise suppression.

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