Related papers: Wavelets on Graphs via Spectral Graph Theory
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…
In this paper we consider the continuous wavelet transform using Gaussian wavelets multiplied by an appropriate rational term. The zeros and poles of this rational modifier act as free parameters and their choice highly influences the shape…
We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The…
We construct and study a class of spectral graph wavelets by analogy with Hermitian wavelets on the real line. We provide a localization result that significantly improves upon those previously available, enabling application to highly…
Defining a sound shift operator for signals existing on a certain graph structure, similar to the well-defined shift operator in classical signal processing, is a crucial problem in graph signal processing, since almost all operations, such…
In the present paper, a construction of spin weighted spherical wavelets is presented. It is based on approximate identities, the wavelets are defined for a continuous set of parameters, and the wavelet transform is invertible directly by…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
Many network datasets exhibit connectivity with variance by resolution and large-scale organization that coexists with localized departures. When vertices have observed ordering or embedding, such as geography in spatial and village…
This work introduces a wavelet neural network to learn a filter-bank specialized to fit non-stationary signals and improve interpretability and performance for digital signal processing. The network uses a wavelet transform as the first…
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 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…
Graph prediction problems prevail in data analysis and machine learning. The inverse prediction problem, namely to infer input data from given output labels, is of emerging interest in various applications. In this work, we develop…
The graph Laplacian operator is widely studied in spectral graph theory largely due to its importance in modern data analysis. Recently, the Fourier transform and other time-frequency operators have been defined on graphs using Laplacian…
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…
Despite their theoretical advantages, spectral methods based on the graph Fourier transform (GFT) are seldom used in graph neural networks (GNNs) due to the cost of computing the eigenbasis and the lack of vertex-domain locality in spectral…
Curvelets are efficient to represent highly anisotropic signal content, such as a local linear and curvilinear structure. First-generation curvelets on the sphere, however, suffered from blocking artefacts. We present a new…
In this paper, we redefine the Graph Fourier Transform (GFT) under the DSP$_\mathrm{G}$ framework. We consider the Jordan eigenvectors of the directed Laplacian as graph harmonics and the corresponding eigenvalues as the graph frequencies.…
We build interpretable and lightweight transformer-like neural networks by unrolling iterative optimization algorithms that minimize graph smoothness priors -- the quadratic graph Laplacian regularizer (GLR) and the $\ell_1$-norm graph…
The newly realized twisted graphene systems such as twisted bilayer graphene (TBG), twisted double bilayer graphene (TDBG), and twisted trilayer graphene (TTG) have attracted widespread theoretical attention. Therefore, a simple and…
We establish that a simple polynomial-time algorithm that we call reweighted spectral partitioning obtains small 2/3-balanced vertex-separators for a number of graph classes, including $O(\sqrt{n})$-sized separators for planar graphs,…