Sampling in paley-wiener spaces on combinatorial graphs

By Isaac Z. Pesenson. 2008

257 citations recorded by the source corpus.

A notion of Paley-Wiener spaces on combinatorial graphs is introduced. It is shown that functions from some of these spaces are uniquely determined by their values on some sets of vertices which are called the uniqueness sets. Such uniqueness sets are described in terms of Poincare-Wirtinger-type inequalities. A reconstruction algorithm of Paley-Wiener functions from uniqueness sets which uses the idea of frames in Hilbert spaces is developed. Special consideration is given to the n-dimensional lattice, homogeneous trees, and eigenvalue and eigenfunction problems on finite graphs.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/cf632cadcd39033886617f4b7b4dd8473781230b

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In Applied Mathematics

In Computational Theory and Mathematics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies (2015, background): “I. INTRODUCTION Graphs provide a natural representation for data in many applications, such as social networks, web information analysis, sensor networks and machine learning [1], [2].”
Graph Signal Processing: Overview, Challenges, and Applications (2017, background): “The first problem formulation and a sufficient condition for unique recovery were presented in [48].”
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains (2012, background): “Finally, in a closely related topic, Pesenson (e.g., [52]) has extended the concept of bandlimited sampling to signals deﬁned on graphs by showing that certain classes of signals can be downsampled on particular subgraphs and then stably reconstructed from the reduced set of samples.”
Discrete Signal Processing on Graphs: Sampling Theory (2015, background): “Recent work involves graph-based filtering [5], [6], [7], graph-based transforms [5], [8], [9], sampling and interpolation on graphs [10], [11], [12], uncertainty principle”
Signals on Graphs: Uncertainty Principle and Sampling (2015, background): “Alternative deﬁnitions of GFT have been proposed, see, e.g., [1]–[7], looking at the problem from different perspectives: [1], [5], [6] apply to undirected graphs and build on the spectral clustering properties of the Laplacian eigenvectors and the minimization of the 2 -norm graph total variation;…”
Signal Recovery on Graphs: Variation Minimization (2014, background): “Recent work involves graph-based ﬁltering [3], [7], [8], graph-based transforms [3], [6], [9], sampling and interpolation on graphs [10]–[12], uncertainty principle on graphs [13], semi-supervised classiﬁcation on graphs [14]–[16], graph dictionary learning [17], [18], and community detection on…”