Related papers: Frames for signal processing on Cayley graphs
Spectral algorithms, such as principal component analysis and spectral clustering, typically require careful data transformations to be effective: upon observing a matrix $A$, one may look at the spectrum of $\psi(A)$ for a properly chosen…
To analyze data supported by arbitrary graphs G, DSP has been extended to Graph Signal Processing (GSP) by redefining traditional DSP concepts like shift, filtering, and Fourier transform among others. This paper revisits modulation,…
Over the last decade, signal processing on graphs has become a very active area of research. Specifically, the number of applications, for instance in statistical or deep learning, using frames built from graphs, such as wavelets on graphs,…
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…
The goal of this paper is to establish the fundamental tools to analyze signals defined over a topological space, i.e. a set of points along with a set of neighborhood relations. This setup does not require the definition of a metric and…
Spectral approaches of network analysis heavily rely upon the eigendecomposition of the graph Laplacian. For instance, in graph signal processing, the Laplacian eigendecomposition is used to define the graph Fourier transform and then…
Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph…
This is the second part of the paper that provides a new strategy for the heterogeneous change detection (HCD) problem, that is, solving HCD from the perspective of graph signal processing (GSP). We construct a graph to represent the…
Frames are the foundation of the linear operators used in the decomposition and reconstruction of signals, such as the discrete Fourier transform, Gabor, wavelets, and curvelet transforms. The emergence of sparse representation models has…
The paper presents the graph signal processing (GSP) companion model that naturally replicates the basic tenets of classical signal processing (DSP) for GSP. The companion model shows that GSP can be made equivalent to DSP 'plus'…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
Data are represented as graphs in a wide range of applications, such as Computer Vision (e.g., images) and Graphics (e.g., 3D meshes), network analysis (e.g., social networks), and bio-informatics (e.g., molecules). In this context, our…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
We consider statistical graph signal processing (GSP) in a generalized framework where each vertex of a graph is associated with an element from a Hilbert space. This general model encompasses various signals such as the traditional…
A number of applications in engineering, social sciences, physics, and biology involve inference over networks. In this context, graph signals are widely encountered as descriptors of vertex attributes or features in graph-structured data.…
This paper investigates the problem of graph signal recovery (GSR) when the topology of the graph is not known in advance. In this paper, the elements of the weighted adjacency matrix is statistically related to normal distribution and the…
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 has become an essential tool for analyzing data structured on irregular domains. While conventional graph shift operators (GSOs) are effective for certain tasks, they inherently lack flexibility in modeling…
The graph Laplacian is an important tool in Graph Signal Processing (GSP) as its eigenvalue decomposition acts as an analogue to the Fourier transform and is known as the Graph Fourier Transform (GFT). The line graph has a GFT that is a…
While a common assumption in graph signal analysis is the smoothness of the signals or the band-limitedness of their spectrum, in many instances the spectrum of real graph data may be concentrated at multiple regions of the spectrum,…