Hierarchical Isometry Properties of Hierarchical Measurements
Abstract
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.
Keywords
Cite
@article{arxiv.2005.10379,
title = {Hierarchical Isometry Properties of Hierarchical Measurements},
author = {Axel Flinth and Benedikt Groß and Ingo Roth and Jens Eisert and Gerhard Wunder},
journal= {arXiv preprint arXiv:2005.10379},
year = {2022}
}
Comments
22 pages, 5 figures. v3: Significant rework of previous version. Section on incoherent blocks added, as well as more numerical experiments. v4: Revision of the manuscript. Several previous mistakes have been corrected