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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Bibliographic Details
Published in:Applied and computational harmonic analysis Vol. 58; pp. 27 - 49
Main Authors: Flinth, Axel, Groß, Benedikt, Roth, Ingo, Eisert, Jens, Wunder, Gerhard
Format: Journal Article
Language:English
Published: Elsevier Inc 01.05.2022
Subjects:
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
Online Access:Get full text
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Summary: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