Related papers: Splines and Wavelets on Circulant Graphs
In this work, we propose a class of spline-like wavelet filterbanks for graph signals. These filterbanks possess the properties of critical sampling and perfect reconstruction. Besides, the analysis filters are localized in the graph domain…
Graph convolutional neural networks (GCNNs) have been widely used in graph learning. It has been observed that the smoothness functional on graphs can be defined in terms of the graph Laplacian. This fact points out in the direction of…
In this paper, we present a new method for designing wavelet filter banks for any dilation matrices and in any dimension. Our approach utilizes extended Laplacian pyramid matrices to achieve this flexibility. By generalizing recent tight…
With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of…
We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely…
To address the limitations of conventional critically sampled graph filter banks in joint time-vertex signal processing, which require decomposing the joint graph into bipartite subgraphs and thus cannot fully exploit all temporal and…
Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include…
In network science, the interplay between dynamical processes and the underlying topologies of complex systems has led to a diverse family of models with different interpretations. In graph signal processing, this is manifested in the form…
This paper focuses on devising graph signal processing tools for the treatment of data defined on the edges of a graph. We first show that conventional tools from graph signal processing may not be suitable for the analysis of such signals.…
In this work we propose the construction of two-channel wavelet filterbanks for analyzing functions defined on the vertices of any arbitrary finite weighted undirected graph. These graph based functions are referred to as graph-signals as…
We develop wavelet representations for edge-flows on simplicial complexes, using ideas rooted in combinatorial Hodge theory and spectral graph wavelets. We first show that the Hodge Laplacian can be used in lieu of the graph Laplacian to…
The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful…
Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural…
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…
We introduce a set of novel multiscale basis transforms for signals on graphs that utilize their "dual" domains by incorporating the "natural" distances between graph Laplacian eigenvectors, rather than simply using the eigenvalue ordering.…
We investigate a scalable $M$-channel critically sampled filter bank for graph signals, where each of the $M$ filters is supported on a different subband of the graph Laplacian spectrum. For analysis, the graph signal is filtered on each…
A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimises the choice of wavelet for a dataset of graphs, such that their…
Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them, to extract specific part out of them, or by changing their domain of representation, using some transformation or…
Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes…
We introduce a new wavelet transform suitable for analyzing functions on point clouds and graphs. Our construction is based on a generalization of the average interpolating refinement scheme of Donoho. The most important ingredient of the…