8 research outputs found
Spectral Domain Spline Graph Filter Bank
In this paper, we present a structure for two-channel spline graph filter
bank with spectral sampling (SGFBSS) on arbitrary undirected graphs. Our
proposed structure has many desirable properties; namely, perfect
reconstruction, critical sampling in spectral domain, flexibility in choice of
shape and cut-off frequency of the filters, and low complexity implementation
of the synthesis section, thanks to our closed-form derivation of the synthesis
filter and its sparse structure. These properties play a pivotal role in
multi-scale transforms of graph signals. Additionally, this framework can use
both normalized and non-normalized Laplacian of any undirected graph. We
evaluate the performance of our proposed SGFBSS structure in nonlinear
approximation and denoising applications through simulations. We also compare
our method with the existing graph filter bank structures and show its superior
performance.Comment: 5 pages, 6 figures, and one tabl
Graph Signal Processing: Overview, Challenges and Applications
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 processing. We then summarize recent developments in developing
basic GSP tools, including methods for sampling, filtering or graph learning.
Next, we review progress in several application areas using GSP, including
processing and analysis of sensor network data, biological data, and
applications to image processing and machine learning. We finish by providing a
brief historical perspective to highlight how concepts recently developed in
GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE
A Review of Graph Neural Networks and Their Applications in Power Systems
Deep neural networks have revolutionized many machine learning tasks in power
systems, ranging from pattern recognition to signal processing. The data in
these tasks is typically represented in Euclidean domains. Nevertheless, there
is an increasing number of applications in power systems, where data are
collected from non-Euclidean domains and represented as graph-structured data
with high dimensional features and interdependency among nodes. The complexity
of graph-structured data has brought significant challenges to the existing
deep neural networks defined in Euclidean domains. Recently, many publications
generalizing deep neural networks for graph-structured data in power systems
have emerged. In this paper, a comprehensive overview of graph neural networks
(GNNs) in power systems is proposed. Specifically, several classical paradigms
of GNNs structures (e.g., graph convolutional networks) are summarized, and key
applications in power systems, such as fault scenario application, time series
prediction, power flow calculation, and data generation are reviewed in detail.
Furthermore, main issues and some research trends about the applications of
GNNs in power systems are discussed
Extending Classical Multirate Signal Processing Theory to Graphs - Part I: Fundamentals
Signal processing on graphs finds applications in many areas. In recent years renewed interest on this topic was kindled by two groups of researchers. Narang and Ortega constructed two-channel filter banks on bipartitie graphs described by Laplacians. Sandryhaila and Moura developed the theory of linear systems, filtering, and frequency responses for the case of graphs with arbitrary adjacency matrices, and showed applications in signal compression, prediction, etc. Inspired by these contributions, this paper extends classical multirate signal processing ideas to graphs. The graphs are assumed to be general with a possibly non-symmetric and complex adjacency matrix. The paper revisits ideas such as noble identities, aliasing, and polyphase decompositions in graph multirate systems. Drawing such a parallel to classical systems allows one to design filter banks with polynomial filters, with lower complexity than arbitrary graph filters. It is shown that the extension of classical multirate theory to graphs is nontrivial, and requires certain mathematical restrictions on the graph. Thus, classical noble identities cannot be taken for granted. Similarly, one cannot claim that the so-called delay chain system is a perfect reconstruction system (as in classical filter banks). It will also be shown that M-partite extensions of the bipartite filter bank results will not work for M-channel filter banks, but a more restrictive condition called M-block cyclic property should be imposed. Such graphs are studied in detail. A detailed theory for M-channel filter banks is developed in a companion paper
Extending Classical Multirate Signal Processing Theory to Graphs - Part I: Fundamentals
Signal processing on graphs finds applications in many areas. In recent years renewed interest on this topic was kindled by two groups of researchers. Narang and Ortega constructed two-channel filter banks on bipartitie graphs described by Laplacians. Sandryhaila and Moura developed the theory of linear systems, filtering, and frequency responses for the case of graphs with arbitrary adjacency matrices, and showed applications in signal compression, prediction, etc. Inspired by these contributions, this paper extends classical multirate signal processing ideas to graphs. The graphs are assumed to be general with a possibly non-symmetric and complex adjacency matrix. The paper revisits ideas such as noble identities, aliasing, and polyphase decompositions in graph multirate systems. Drawing such a parallel to classical systems allows one to design filter banks with polynomial filters, with lower complexity than arbitrary graph filters. It is shown that the extension of classical multirate theory to graphs is nontrivial, and requires certain mathematical restrictions on the graph. Thus, classical noble identities cannot be taken for granted. Similarly, one cannot claim that the so-called delay chain system is a perfect reconstruction system (as in classical filter banks). It will also be shown that M-partite extensions of the bipartite filter bank results will not work for M-channel filter banks, but a more restrictive condition called M-block cyclic property should be imposed. Such graphs are studied in detail. A detailed theory for M-channel filter banks is developed in a companion paper