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Sampling and Reconstruction by Means of Weighted Inverses

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Abstract

In this article, we address the problem of reconstructing an element in a Hilbert space from its samples by means of a weighted least square approximation. We show how this problem is linked with the notions of weighted inverses, weighted projections and an angle condition known as compatibility. In addition, we study perfect reconstruction operators and their relationship with the previous problem. Finally, since the reconstructions through these approaches may not be unique, we propose different criteria for choosing an optimal one among all of them.

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Correspondence to M. Laura Arias.

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Communicated by Akram Aldroubi.

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The authors were partially supported by CONICET (PIP 11220120100426), FONCYT (PICT 2017-0883 and 2014-1776.

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Arias, M.L., Gonzalez, M.C. Sampling and Reconstruction by Means of Weighted Inverses. J Fourier Anal Appl 26, 41 (2020). https://doi.org/10.1007/s00041-020-09747-5

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  • DOI: https://doi.org/10.1007/s00041-020-09747-5

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