Related papers: Spectral Domain Spline Graph Filter Bank

Designing distributed optimal controllers subject to communication constraints is a difficult problem unless structural assumptions are imposed on the underlying dynamics and information exchange structure, e.g., sparsity, delay, or spatial…

Sampling of signals belonging to a low-dimensional subspace has well-documented merits for dimensionality reduction, limited memory storage, and online processing of streaming network data. When the subspace is known, these signals can be…

The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in…

Graph neural networks (GNNs) have emerged as a powerful tool for nonlinear processing of graph signals, exhibiting success in recommender systems, power outage prediction, and motion planning, among others. GNNs consists of a cascade of…

We turn a given filter bank into a filtering scheme that provides perfect reconstruction, synthesis is the adjoint of the analysis part (so-called unitary filter banks), all filters have equal norm, and the essential features of the…

The graph Fourier transform (GFT) is a fundamental tool in graph signal processing and has recently been extended to the graph fractional Fourier transform (GFRFT). Existing sampling methods in the GFRFT domain are primarily designed to…

Graph Neural Networks (GNNs) have shown considerable effectiveness in a variety of graph learning tasks, particularly those based on the message-passing approach in recent years. However, their performance is often constrained by a limited…

Graphs are naturally used to describe the structures of various real-world systems in biology, society, computer science etc., where subgraphs or motifs as basic blocks play an important role in function expression and information…

We study the problem of selecting the best sampling set for bandlimited reconstruction of signals on graphs. A frequency domain representation for graph signals can be defined using the eigenvectors and eigenvalues of variation operators…

Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to…

This paper proposes a blind detection problem for low pass graph signals. Without assuming knowledge of the exact graph topology, we aim to detect if a set of graph signal observations are generated from a low pass graph filter. Our problem…

The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round…

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general…

Recent spectral graph sparsification research allows constructing nearly-linear-sized subgraphs that can well preserve the spectral (structural) properties of the original graph, such as the first few eigenvalues and eigenvectors of the…

We propose a framework for generalized sampling of graph signals that parallels sampling in shift-invariant (SI) subspaces. This framework allows for arbitrary input signals, which are not constrained to be bandlimited. Furthermore, the…

Graph Neural Networks (GNNs) have achieved remarkable success in various graph-based learning tasks. While their performance is often attributed to the powerful neighborhood aggregation mechanism, recent studies suggest that other…

FPGAs are well established in the signal processing domain, where their fine-grained programmable nature allows the inherent parallelism in these applications to be exploited for enhanced performance. As architectures have evolved, FPGA…

Graph Fourier transform (GFT) is one of the fundamental tools in graph signal processing to decompose graph signals into different frequency components and to represent graph signals with strong correlation by different modes of variation…

Spectral Graph Neural Network is a kind of Graph Neural Network (GNN) based on graph signal filters. Some models able to learn arbitrary spectral filters have emerged recently. However, few works analyze the expressive power of spectral…

Graph signal processing (GSP) is an emerging field developed for analyzing signals defined on irregular spatial structures modeled as graphs. Given the considerable literature regarding the resilience of infrastructure networks using graph…