Hierarchical isometry properties of hierarchical measurements

Flinth A, Gross B, Roth I, Eisert J, Wunder G (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Applied and Computational Harmonic Analysis Elsevier

Book Volume: 58

Pages Range: 27-49

DOI: 10.1016/j.acha.2021.12.006

Abstract

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.

Involved external institutions

Chalmers University of Technology / Chalmers tekniska högskola SE Sweden (SE) Freie Universität Berlin DE Germany (DE)

How to cite

APA:

Flinth, A., Gross, B., Roth, I., Eisert, J., & Wunder, G. (2022). Hierarchical isometry properties of hierarchical measurements. Applied and Computational Harmonic Analysis, 58, 27-49. https://dx.doi.org/10.1016/j.acha.2021.12.006

MLA:

Flinth, Axel, et al. "Hierarchical isometry properties of hierarchical measurements." Applied and Computational Harmonic Analysis 58 (2022): 27-49.

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