相关论文: Multi-dimensional Graph Linear Canonical Transform

Discrete trigonometric transforms (DTTs), such as the DCT-2 and the DST-7, are widely used in video codecs for their balance between coding performance and computational efficiency. In contrast, data-dependent transforms, such as the…

Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…

This paper introduces a $\textit{canonical}$ graph signal model defined by a $\textit{canonical}$ graph and a $\textit{canonical}$ shift, the $\textit{companion}$ graph and the $\textit{companion}$ shift. These are canonical because, under…

Long Time Coherent Integration (LTCI) aims to accumulate target energy through long time integration, which is an effective method for the detection of a weak target. However, for a moving target, defocusing can occur due to range migration…

Domain decomposition methods (DDMs) are popular solvers for discretized systems of partial differential equations (PDEs), with one-level and multilevel variants. These solvers rely on several algorithmic and mathematical parameters,…

Spherical functions appear throughout computer graphics, from spherical harmonic lighting and precomputed radiance transfer to neural radiance fields and procedural planet rendering. Efficient evaluation is critical for real-time…

Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each…

We introduce a new class of multilevel, adaptive, dual-space methods for computing fast convolutional transforms. These methods can be applied to a broad class of kernels, from the Green's functions for classical partial differential…

The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed…

In recent years there has been a renewed interest in finding fast algorithms to compute accurately the linear canonical transform (LCT) of a given function. This is driven by the large number of applications of the LCT in optics and signal…

The graph fractional Fourier transform (GFRFT) applies a single global fractional order to all graph frequencies, which restricts its adaptability to diverse signal characteristics across the spectral domain. To address this limitation, in…

In recent years, multiple sensor-based devices and systems have been deployed in smart agriculture, industrial automation, E-Health, etc. The diversity of sensor data types and the amount of data pose critical challenges for data…

We propose new graph representations that exploit dense local structure to improve time and space simultaneously. Given an undirected graph $G$, we define a dual clique cover (DCC) representation of $G$ to be the pair $(C, L)$, where $C$ is…

This paper presents the novel Dual Stream Graph-Transformer Fusion (DS-GTF) architecture designed specifically for classifying task-based Magnetoencephalography (MEG) data. In the spatial stream, inputs are initially represented as graphs,…

Convolutional neural networks (CNNs) leverage the great power in representation learning on regular grid data such as image and video. Recently, increasing attention has been paid on generalizing CNNs to graph or network data which is…

Graph Convolutional Networks (GCNs) have attracted more and more attentions in recent years. A typical GCN layer consists of a linear feature propagation step and a nonlinear transformation step. Recent works show that a linear GCN can…

With the development of data acquisition technology, large amounts of multi-channel data are collected and widely used in many fields. Most of them, such as RGB images and vector fields, can be expressed as different types of multi-channel…

Low-rank approximation models of data matrices have become important machine learning and data mining tools in many fields including computer vision, text mining, bioinformatics and many others. They allow for embedding high-dimensional…

We consider the problem of layering general directed graphs under height and possibly also width constraints. Given a directed graph G = (V,A) and a maximal height, we propose a layering approach that minimizes a weighted sum of the number…

We propose novel dynamic multiscale graph neural networks (DMGNN) to predict 3D skeleton-based human motions. The core idea of DMGNN is to use a multiscale graph to comprehensively model the internal relations of a human body for motion…