Sampling in paley-wiener spaces on combinatorial graphs

2011/11/25 by Isaac Z. Pesenson, Pesenson, Isaac · 7 citations
Computer Science · Mathematics · Medicine · #FOS: Mathematics #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Spectral Theory (math.SP) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1111.5896

openalex publication_date 2011/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A notion of Paley-Wiener spaces is introduced on combinatorial graphs. 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-Wirtingertype 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 n-dimensional lattice, homogeneous trees, and eigenvalue and eigenfunction problems on finite graphs.

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• Bayesian Convolutional Neural Networks for Prior Learning in Graph Signal Recovery
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