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Algebraic compressed sensing

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2023

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Breiding, Paul
Gesmundo, Fulvio
Vannieuwenhoven, Nick

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Applied and Computational Harmonic Analysis. Elsevier. 2023, 65, pp. 374-406. ISSN 1063-5203. eISSN 1096-603X. Available under: doi: 10.1016/j.acha.2023.03.006

Zusammenfassung

We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for instance, low-rank matrix and tensor recovery. We employ powerful techniques from algebraic geometry to study well-posedness of sufficiently general compressed sensing problems, including existence, local recoverability, global uniqueness, and local smoothness. Our main results are summarized in thirteen questions and answers in algebraic compressed sensing. Most of our answers concerning the minimum number of required measurements for existence, recoverability, and uniqueness of algebraic compressed sensing problems are optimal and depend only on the dimension of the model.

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510 Mathematik

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ISO 690BREIDING, Paul, Fulvio GESMUNDO, Mateusz MICHALEK, Nick VANNIEUWENHOVEN, 2023. Algebraic compressed sensing. In: Applied and Computational Harmonic Analysis. Elsevier. 2023, 65, pp. 374-406. ISSN 1063-5203. eISSN 1096-603X. Available under: doi: 10.1016/j.acha.2023.03.006
BibTex
@article{Breiding2023Algeb-66966,
  year={2023},
  doi={10.1016/j.acha.2023.03.006},
  title={Algebraic compressed sensing},
  volume={65},
  issn={1063-5203},
  journal={Applied and Computational Harmonic Analysis},
  pages={374--406},
  author={Breiding, Paul and Gesmundo, Fulvio and Michalek, Mateusz and Vannieuwenhoven, Nick}
}
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