相关论文: A Design of Denser-Graph-Frequency Graph Fourier F…

Fuzzy systems (FSs) have enjoyed wide applications in various fields, including pattern recognition, intelligent control, data mining and bioinformatics, which is attributed to the strong interpretation and learning ability. In traditional…

The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…

The short-time Fourier transform (STFT) is widely used for analyzing non-stationary signals. However, its performance is highly sensitive to its parameters, and manual or heuristic tuning often yields suboptimal results. To overcome this…

With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of…

In this paper, we focus on Fourier analysis and holographic transforms for signal representation. For instance, in the case of image processing, the holographic representation has the property that an arbitrary portion of the transformed…

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…

Graph embedding techniques have been increasingly deployed in a multitude of different applications that involve learning on non-Euclidean data. However, existing graph embedding models either fail to incorporate node attribute information…

We present the Evolving Graph Fourier Transform (EFT), the first invertible spectral transform that captures evolving representations on temporal graphs. We motivate our work by the inadequacy of existing methods for capturing the evolving…

This paper develops fast graph Fourier transform (GFT) algorithms with O(n log n) runtime complexity for rank-one updates of the path graph. We first show that several commonly-used audio and video coding transforms belong to this class of…

The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal…

Many experiments, and in particular gravitational wave detectors, produce continuous streams of data whose frequency representations contain discrete, relatively narrowband coherent features at high amplitude. We discuss the application of…

Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…

Choosing an appropriate frequency definition and norm is critical in graph signal sampling and reconstruction. Most previous works define frequencies based on the spectral properties of the graph and use the same frequency definition and…

Narrowing the performance gap between optimal and feasible detection in inter-symbol interference (ISI) channels, this paper proposes to use graph neural networks (GNNs) for detection that can also be used to perform joint detection and…

Graph neural networks (GNNs) have become a workhorse approach for learning from data defined over irregular domains, typically by implicitly assuming that the data structure is represented by a homophilic graph. However, recent works have…

Classical spectral graph theory relies on the symmetry of the adjacency and Laplacian operators, which guarantees orthogonal eigenbases and energy-preserving Fourier transforms. However, real-world networks are intrinsically directed and…

Spectral graph convolution, an important tool of data filtering on graphs, relies on two essential decisions: selecting spectral bases for signal transformation and parameterizing the kernel for frequency analysis. While recent techniques…

Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…

We propose a new point of view in the study of Fourier analysis on graphs, taking advantage of localization in the Fourier domain. For a signal $f$ on vertices of a weighted graph $\mathcal{G}$ with Laplacian matrix $\mathcal{L}$, standard…