Hierarchical isometry properties of hierarchical measurements
Journal article, 2022

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.

Thresholding algorithms

Structured compressed sensing

Block detection

Hierarchical sparsity

Internet of Things

MiMO

Author

Axel Flinth

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering, Computer vision and medical image analysis

Benedikt Groß

Freie Universität Berlin

Ingo Roth

Technology Innovation Institute

Freie Universität Berlin

Jens Eisert

Freie Universität Berlin

Gerhard Wunder

Freie Universität Berlin

Applied and Computational Harmonic Analysis

1063-5203 (ISSN) 1096-603X (eISSN)

Vol. 58 27-49

Subject Categories

Computational Mathematics

Mathematical Analysis

DOI

10.1016/j.acha.2021.12.006

More information

Latest update

1/10/2022