相关论文: Towards a characterization of the uncertainty curv…

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.…

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…

Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such…

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…

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…

We expand upon a graph theoretic set of uncertainty principles with tight bounds for difference estimators acting simultaneously in the graph domain and the frequency domain. We show that the eigenfunctions of a modified graph Laplacian and…

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…

In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and…

In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this…

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…

Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image…

Graph signal processing deals with signals which are observed on an irregular graph domain. While many approaches have been developed in classical graph theory to cluster vertices and segment large graphs in a signal independent way, signal…

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…

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…

We propose Gaussian processes for signals over graphs (GPG) using the apriori knowledge that the target vectors lie over a graph. We incorporate this information using a graph- Laplacian based regularization which enforces the target…

The emerging field of graph signal processing (GSP) allows to transpose classical signal processing operations (e.g., filtering) to signals on graphs. The GSP framework is generally built upon the graph Laplacian, which plays a crucial role…

Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph…

Graph signal processing (GSP) studies graph-structured data, where the central concept is the vector space of graph signals. To study a vector space, we have many useful tools up our sleeves. However, uncertainty is omnipresent in practice,…

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-…

Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…