Graph Signal Sampling and Interpolation Based on Clusters and Averages

Pesenson, Isaac Z.; Pesenson, Meyer Z.

doi:10.1007/s00041-021-09828-z

Cited by 7 publications

(4 citation statements)

References 39 publications

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“…Developing methods to identify suitable bases or frames for low-spectrum Paley-Wiener spaces is an important area of research in graph signal processing, particularly in the case of clustered but otherwise general graphs (e.g, [32]). Analogues of Slepian-type eigenfunctions on graphs [8,9] are a relatively new aspect of this.…”

Section: Discussionmentioning

confidence: 99%

Spatio–Spectral Limiting on Replacements of Tori by Cubes

Hogan,

Lakey

2023

Mathematics

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A class of graphs is defined in which each vertex of a discrete torus is replaced by a Boolean hypercube in such a way that vertices in a fixed subset of each replacement cube are adjacent to corresponding vertices of a neighboring replacement cube. Bases of eigenvectors of the Laplacians of the resulting graphs are described in a manner suitable for quantifying the concentration of a low-spectrum vertex function on a single vertex replacement. Functions that optimize this concentration on these graphs can be regarded as analogues of Slepian prolate functions that optimize concentration of a bandlimited signal on an interval in the classical setting of the real line. Comparison to the case of a simple discrete cycle shows that replacement allows for higher concentration.

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Section: Discussionmentioning

confidence: 99%

Spatio–Spectral Limiting on Replacements of Tori by Cubes

Hogan,

Lakey

2023

Mathematics

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“…Note, that all the inequalities in this Theorem are some sort of generalized Poincaré-type inequality since they contain estimates of a function through its gradient. Using these estimates the next statement about a Plancherel-Polya-type (or Marcinkiewicz-Zygmund, or frame) inequalities can be proved (see [17]). For every f ∈ E ω (G) with ω satisfying…”

Section: A Poincare-type Inequality For Finite Graphsmentioning

confidence: 99%

“…Section 7.1 contains a proof of Lemma 3.2. Methodologically this paper is a combination of several ideas from the articles [8] and [17].…”

Section: Introductionmentioning

confidence: 99%

Average sampling and average splines on combinatorial graphs

Pesenson

2019

2019 13th International Conference on Sampling Theory and Applications (SampTA)

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For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are suggested. The first two of them are using language of dual Hilbert frames and the so-called frame algorithm respectively. The third one is using the so-called weighted variational interpolating splines which are constructed in the setting of combinatorial graphs. This development requires a new set of Poincaré-type inequalities which we prove for functions on combinatorial graphs.

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“…Graph signal processing is a cutting-edge research field for the study of graph signals in which mathematical processing tools as filtering, compression, noise removal, sampling, or decomposition methods are investigated [6,11,[22][23][24]26,33,35]. Graph structures appear naturally in a multitude of modern applications, as in social net- works, traffic maps or biological networks.…”

Section: Introductionmentioning

confidence: 99%

Partition of Unity Methods for Signal Processing on Graphs

Cavoretto

Rossi

Erb

2021

J Fourier Anal Appl

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Partition of unity methods (PUMs) on graphs are simple and highly adaptive auxiliary tools for graph signal processing. Based on a greedy-type metric clustering and augmentation scheme, we show how a partition of unity can be generated in an efficient way on graphs. We investigate how PUMs can be combined with a local graph basis function (GBF) approximation method in order to obtain low-cost global interpolation or classification schemes. From a theoretical point of view, we study necessary prerequisites for the partition of unity such that global error estimates of the PUM follow from corresponding local ones. Finally, properties of the PUM as cost-efficiency and approximation accuracy are investigated numerically. KeywordsPartition of unity method (PUM) • Graph signal processing • Graph basis functions (GBFs) • Kernel-based approximation and interpolation • Spectral graph theory B Wolfgang Erb

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Graph Signal Sampling and Interpolation Based on Clusters and Averages

Cited by 7 publications

References 39 publications

Spatio–Spectral Limiting on Replacements of Tori by Cubes

Spatio–Spectral Limiting on Replacements of Tori by Cubes

Average sampling and average splines on combinatorial graphs

Partition of Unity Methods for Signal Processing on Graphs

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