Related papers: Global and Local Uncertainty Principles for Signal…
Uncertainty principles present an important theoretical tool in signal processing, as they provide limits on the time-frequency concentration of a signal. In many real-world applications the signal domain has a complicated irregular…
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…
We present an uncertainty principle for graph signals in the vertex-time domain, unifying the classical time-frequency and graph uncertainty principles within a single framework. By defining vertex-time and spectral-frequency spreads, we…
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…
In many applications, from sensor to social networks, gene regulatory networks or big data, observations can be represented as a signal defined over the vertices of a graph. Building on the recently introduced Graph Fourier Transform, the…
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…
The uncertainty principle states that a signal cannot be localized both in time and frequency. With the aim of extending this result to signals on graphs, Agaskar&Lu introduce notions of graph and spectral spreads. They show that a graph…
Signal processing on graphs is a recent research domain that aims at generalizing classical tools in signal processing, in order to analyze signals evolving on complex domains. Such domains are represented by graphs, for which one can…
We present a flexible framework for uncertainty principles in spectral graph theory. In this framework, general filter functions modeling the spatial and spectral localization of a graph signal can be incorporated. It merges several…
With an increasing influx of classical signal processing methodologies into the field of graph signal processing, approaches grounded in discrete linear canonical transform have found application in graph signals. In this paper, we…
By use of window functions, time-frequency analysis tools like Short Time Fourier Transform overcome a shortcoming of the Fourier Transform and enable us to study the time- frequency characteristics of signals which exhibit transient os-…
While uncertainty estimation for graphs recently gained traction, most methods rely on homophily and deteriorate in heterophilic settings. We address this by analyzing message passing neural networks from an information-theoretic…
The Heisenberg Uncertainty Principle (HUP) limits the accuracy in the simultaneous measurements of the position and momentum variables of any quantum system. This is known to be true in the context of non-relativistic quantum mechanics.…
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…
Uncertainty principles for concentration of signals into truncated subspaces are considered. The ``classic'' uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem…
A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg's uncertainty principle states that a given function cannot be arbitrarily compact both in time and…
The classical support uncertainty principle states that the signal and its discrete Fourier transform (DFT) cannot be localized simultaneously in an arbitrary small area in the time and the frequency domain. The product of the number of…
Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we…
We introduce a novel method, called Dispersion Entropy for Graph Signals, $DE_G$, as a powerful tool for analysing the irregularity of signals defined on graphs. We demonstrate the effectiveness of $DE_G$ in detecting changes in the…
As a time-shifted and frequency-modulated version of the linear canonical transform (LCT), the offset linear canonical transform (OLCT) provides a more general framework of most existing linear integral transforms in signal processing and…