Related papers: Fourier transform of vector-valued graph signals
We propose a desigining method of a flexible sampling operator for graph signals via a difference-of-convex (DC) optimization algorithm. A fundamental challenge in graph signal processing is sampling, especially for graph signals that are…
With the advancements in technology and monitoring tools, we often encounter multivariate graph signals, which can be seen as the realizations of multivariate graph processes, and revealing the relationship between their constituent…
A new scheme to sample signals defined in the nodes of a graph is proposed. The underlying assumption is that such signals admit a sparse representation in a frequency domain related to the structure of the graph, which is captured by the…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
Quantum signal processing (QSP) and quantum singular value transformation (QSVT) are powerful techniques for the development of quantum procedures. They allow to derive circuits preparing desired polynomial transformations. Recent research…
When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and…
Reconstructing time-varying graph signals (or graph time-series imputation) is a critical problem in machine learning and signal processing with broad applications, ranging from missing data imputation in sensor networks to time-series…
Deep learning, particularly convolutional neural networks (CNNs), have yielded rapid, significant improvements in computer vision and related domains. But conventional deep learning architectures perform poorly when data have an underlying…
This paper deals with problem of blind identification of a graph filter and its sparse input signal, thus broadening the scope of classical blind deconvolution of temporal and spatial signals to irregular graph domains. While the…
In this paper, we propose a new regression-based algorithm to compute Graph Fourier Transform (GFT). Our algorithm allows different regularizations to be included when computing the GFT analysis components, so that the resulting components…
The definition of the graph Fourier transform is a fundamental issue in graph signal processing. Conventional graph Fourier transform is defined through the eigenvectors of the graph Laplacian matrix, which minimize the $\ell_2$ norm signal…
This paper provides an overview of the current landscape of signal processing (SP) on directed graphs (digraphs). Directionality is inherent to many real-world (information, transportation, biological) networks and it should play an…
Graph signal processing (GSP) has become an important tool in image processing because of its ability to reveal underlying data structures. Many real-life multimedia datasets, however, exhibit heterogeneous structures across frames.…
We introduce graph gamma process (GGP) linear dynamical systems to model real-valued multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a…
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…
We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a recently introduced measure-theoretic view of transformers. A…
In many domains data is currently represented as graphs and therefore, the graph representation of this data becomes increasingly important in machine learning. Network data is, implicitly or explicitly, always represented using a graph…
Graph transformers are a recent advancement in machine learning, offering a new class of neural network models for graph-structured data. The synergy between transformers and graph learning demonstrates strong performance and versatility…
In graph neural networks (GNNs), both node features and labels are examples of graph signals, a key notion in graph signal processing (GSP). While it is common in GSP to impose signal smoothness constraints in learning and estimation tasks,…
For the interpolation of graph signals with generalized shifts of a graph basis function (GBF), we introduce the concept of positive definite functions on graphs. This concept merges kernel-based interpolation with spectral theory on graphs…