Related papers: Graph Fractional Fourier Transform: A Unified and …
Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…
The aim of this chapter is to give an overview of the recent advances related to sampling and recovery of signals defined over graphs. First, we illustrate the conditions for perfect recovery of bandlimited graph signals from samples…
Graph signals arise in various applications, ranging from sensor networks to social media data. The high-dimensional nature of these signals implies that they often need to be compressed in order to be stored and transmitted. The common…
We propose a new point of view in the study of Fourier analysis on graphs, taking advantage of localization in the Fourier domain. For a signal $f$ on vertices of a weighted graph $\mathcal{G}$ with Laplacian matrix $\mathcal{L}$, standard…
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.…
A continuous-time graph signal can be viewed as a time series of graph signals. It generalizes both the classical continuous-time signal and ordinary graph signal. Therefore, such a signal can be considered as a function on two domains: the…
Fourier ptychography (FP) is a recently proposed computational imaging technique for high space-bandwidth product imaging. In real setups such as endoscope and transmission electron microscope, the common sample motion largely degrades the…
As neural networks are increasingly being applied to real-world applications, mechanisms to address distributional shift and sequential task learning without forgetting are critical. Methods incorporating network expansion have shown…
Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…
Recently, graph prompt learning has garnered increasing attention in adapting pre-trained GNN models for downstream graph learning tasks. However, existing works generally conduct prompting over all graph elements (e.g., nodes, edges, node…
Fine-tuning flow matching models is a central challenge in settings with limited data, evolving distributions, or strict efficiency demands, where unconstrained fine-tuning can erode the accuracy and efficiency gains learned during…
We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we…
Graph filtering is the cornerstone operation in graph signal processing (GSP). Thus, understanding it is key in developing potent GSP methods. Graph filters are local and distributed linear operations, whose output depends only on the local…
In this work, we study the properties of sampling sets on families of large graphs by leveraging the theory of graphons and graph limits. To this end, we extend to graphon signals the notion of removable and uniqueness sets, which was…
In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…
Graph signal processing (GSP) is a prominent framework for analyzing signals on non-Euclidean domains. The graph Fourier transform (GFT) uses the combinatorial graph Laplacian matrix to reveal the spectral decomposition of signals in the…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
In this paper, we extend the sampling theory on graphs by constructing a framework that exploits the structure in product graphs for efficient sampling and recovery of bandlimited graph signals that lie on them. Product graphs are graphs…