Hierarchical isometry properties of hierarchical measurements

Compressed sensing studies linear recovery problems under structure assumptions. We introduce a new class of measurement operators, coined hierarchical measurement operators, and prove results guaranteeing the efficient, stable and robust recovery of hierarchically structured signals from such measu...

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Veröffentlicht in:Applied and computational harmonic analysis Jg. 58; S. 27 - 49
Hauptverfasser: Flinth, Axel, Groß, Benedikt, Roth, Ingo, Eisert, Jens, Wunder, Gerhard
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.05.2022
Schlagworte:
Block detection
Hierarchical sparsity
Internet of Things
MiMO
Structured compressed sensing
Thresholding algorithms
Hierarchical sparsity
Thresholding algorithms
Structured compressed sensing
MiMO
Block detection
Internet of Things
ISSN:1063-5203, 1096-603X, 1096-603X
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Zusammenfassung:Compressed sensing studies linear recovery problems under structure assumptions. We introduce a new class of measurement operators, coined hierarchical measurement operators, and prove results guaranteeing the efficient, stable and robust recovery of hierarchically structured signals from such measurements. We derive bounds on their hierarchical restricted isometry properties based on the restricted isometry constants of their constituent matrices, generalizing and extending prior work on Kronecker-product measurements. As an exemplary application, we apply the theory to two communication scenarios. The fast and scalable HiHTP algorithm is shown to be suitable for solving these types of problems and its performance is evaluated numerically in terms of sparse signal recovery and block detection capability.
ISSN:1063-5203
1096-603X
1096-603X
DOI:10.1016/j.acha.2021.12.006