Algebraic compressed sensing

被引：4

作者：

Breiding, Paul ^{[1
]}

Gesmundo, Fulvio ^{[2
]}

Michalek, Mateusz ^{[3
]}

Vannieuwenhoven, Nick ^{[4
,5
]}

机构：

[1] Univ Osnabruck, Fachbereich Math Informat, Albrechtstr 28a, D-49076 Osnabruck, Germany

[2] Saarland Univ, Saarland Informat Campus, D-66123 Saarbrucken, Germany

[3] Univ Konstanz, Dept Math & Stat, Univ str 10, D-78457 Constance, Germany

[4] Katholieke Univ Leuven, Dept Comp Sci, Celestijnenlaan 200A, B-3001 Leuven, Belgium

[5] KU Leuven Inst AI, Leuven AI, B-3000 Leuven, Belgium

来源：

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2023年 / 65卷

关键词：

Algebraic compressed sensing; Recoverability; Identifiability; RANK MATRIX COMPLETION; POLYNOMIAL SYSTEMS; SIGNAL RECOVERY; RANDOM PROJECTIONS; MOMENT VARIETIES; COMPLEXITY; ALGORITHM;

D O I：

10.1016/j.acha.2023.03.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：374 / 406

页数：33

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