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Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal…
In this paper, we introduce several new schemes for calculation of discrete wavelet transforms of images. These schemes reduce the number of steps and, as a consequence, allow to reduce the number of synchronizations on parallel…
In this paper, we completely solve the matrix extension problem with symmetry and provide a step-by-step algorithm to construct such a desired matrix $\mathsf{P}_e$ from a given matrix $\mathsf{P}$. Furthermore, using a cascade structure,…
The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based…
In this paper, we propose a new method for the construction of multi-dimensional, wavelet-like families of affine frames, commonly referred to as framelets, with specific directional characteristics, small and compact support in space,…
Spectral Graph Neural Networks (GNNs), alternatively known as graph filters, have gained increasing prevalence for heterophily graphs. Optimal graph filters rely on Laplacian eigendecomposition for Fourier transform. In an attempt to avert…
Filtering-based graph neural networks (GNNs) constitute a distinct class of GNNs that employ graph filters to handle graph-structured data, achieving notable success in various graph-related tasks. Conventional methods adopt a graph-wise…
The operator-theoretic dichotomy underlying diffusion on directed networks is \emph{symmetry versus non-self-adjointness} of the Markov transition operator. In the reversible (detailed-balance) regime, a directed random walk $P$ is…
Graph convolutional neural network provides good solutions for node classification and other tasks with non-Euclidean data. There are several graph convolutional models that attempt to develop deep networks but do not cause serious…
This paper is the continuation of the work in~\cite{Yin}. In that paper we generalized the definition of $W$-graph ideal in the weighted Coxeter groups, and showed how to construct a $W$-graph from a given $W$-graph ideal in the case of…
Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…
A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…
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…
Dynamic graph signal processing provides a principled framework for analyzing time-varying data defined on irregular graph domains. However, existing joint time-vertex transforms such as the joint time-vertex fractional Fourier transform…
Cardiac Magnetic Resonance (CMR) imaging is widely used for heart model reconstruction and digital twin computational analysis because of its ability to visualize soft tissues and capture dynamic functions. However, CMR images have an…
To address limitations of the graph fractional Fourier transform (GFRFT) Wiener filtering and the traditional joint time-vertex fractional Fourier transform (JFRFT) Wiener filtering, this study proposes a filtering method based on the…
We study blind deconvolution of signals defined on the nodes of an undirected graph. Although observations are bilinear functions of both unknowns, namely the forward convolutional filter coefficients and the graph signal input, a filter…
In this work, we investigated a simple structured graphene terahertz (THz) metasurface (MSF) with perfect absorption, wideband, polarization insensitive, oblique incidence insensitive and frequency reconfiguration. The graphene MSF…
This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general…
Recently, many graph matching methods that incorporate pairwise constraint and that can be formulated as a quadratic assignment problem (QAP) have been proposed. Although these methods demonstrate promising results for the graph matching…