Algebraic compressed sensing
Autor(en): | Breiding, Paul Gesmundo, Fulvio Michalek, Mateusz Vannieuwenhoven, Nick |
Stichwörter: | Algebraic compressed sensing; ALGORITHM; COMPLEXITY; Identifiability; Mathematics; Mathematics, Applied; MOMENT VARIETIES; POLYNOMIAL SYSTEMS; RANDOM PROJECTIONS; RANK MATRIX COMPLETION; Recoverability; SIGNAL RECOVERY | Erscheinungsdatum: | 2023 | Herausgeber: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Journal: | APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | Volumen: | 65 | Startseite: | 374 | Seitenende: | 406 | 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.(c) 2023 Elsevier Inc. All rights reserved. |
ISSN: | 1063-5203 | DOI: | 10.1016/j.acha.2023.03.006 |
Zur Langanzeige
Seitenaufrufe
1
Letzte Woche
0
0
Letzter Monat
0
0
geprüft am 17.05.2024