Related papers: Discrete Linear Canonical Transform on Graphs
The paper presents the graph Fourier transform (GFT) of a signal in terms of its spectral decomposition over the Jordan subspaces of the graph adjacency matrix $A$. This representation is unique and coordinate free, and it leads to…
In this paper, we present a signal processing framework for directed graphs. Unlike undirected graphs, a graph shift operator such as the adjacency matrix associated with a directed graph usually does not admit an orthogonal eigenbasis.…
Current video coding standards, including H.264/AVC, HEVC, and VVC, employ discrete cosine transform (DCT), discrete sine transform (DST), and secondary to Karhunen-Loeve transforms (KLTs) decorrelate the intra-prediction residuals.…
We study decentralized designing of the graph shift operators to implement linear transformations between graph signals. Since this operator captures the local structure of the graph, the proposed method of this paper gives rise to…
As a generalization of the two-dimensional Fourier transform (2D FT) and 2D fractional Fourier transform, the 2D nonseparable linear canonical transform (2D NsLCT) is useful in optics, signal and image processing. To reduce the digital…
The Discrete Gabor Transform (DGT) is the most commonly used transform for signal analysis and synthesis using a linear frequency scale. It turns out that the involved operators are rich in structure if one samples the discrete phase space…
Since the evolution of digital computers, the storage of data has always been in terms of discrete bits that can store values of either 1 or 0. Hence, all computer programs (such as MATLAB), convert any input continuous signal into a…
Linear Canonical Transformations (LCTs) are known in signal processing and optics as the generalization of certain useful integral transforms. In quantum theory, they can be identified as the linear transformations which keep invariant the…
Transformer-based models have recently shown success in representation learning on graph-structured data beyond natural language processing and computer vision. However, the success is limited to small-scale graphs due to the drawbacks of…
Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite…
Graph Transformer (GT) has recently emerged as a promising neural network architecture for learning graph-structured data. However, its global attention mechanism with quadratic complexity concerning the graph scale prevents wider…
Discrete transforms, such as the discrete Fourier transform, are widely used in machine learning to improve model performance by extracting meaningful features. However, with numerous transforms available, selecting an appropriate one often…
Nuclei classification is a critical step in computer-aided diagnosis with histopathology images. In the past, various methods have employed graph neural networks (GNN) to analyze cell graphs that model inter-cell relationships by…
In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this…
We introduce a multi-windowed graph Fourier transform (MWGFT) for the joint vertex-frequency analysis of signals defined on graphs. Building on generalized translation and modulation induced by the graph Laplacian, the proposed framework…
This paper presents a systematic methodology based on the algebraic theory of signal processing to classify and derive fast algorithms for linear transforms. Instead of manipulating the entries of transform matrices, our approach derives…
In many network problems, graphs may change by the addition of nodes, or the same problem may need to be solved in multiple similar graphs. This generates inefficiency, as analyses and systems that are not transferable have to be…
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…
Modern compression systems use linear transformations in their encoding and decoding processes, with transforms providing compact signal representations. While multiple data-dependent transforms for image/video coding can adapt to diverse…
Recent progress in graph signal processing (GSP) has addressed a number of problems, including sampling and filtering. Proposed methods have focused on generic graphs and defined signals with certain characteristics, e.g., bandlimited…