Weighted sampling and weighted interpolation on combinatorial graphs

2019/05/06 by Isaac Z. Pesenson, Pesenson, Isaac Z.
Computer Science · Mathematics · Medicine · #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications

paper · pdf · doi:10.48550/arxiv.1905.02603

openalex publication_date 2019/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains

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