Hierarchical Sparse Recovery from Hierarchically Structured Measurements with Application to Massive Random Access
Paper in proceeding, 2021

A new family of operators, dubbed hierarchical measurement operators, is introduced and discussed within the framework of hierarchically sparse recovery. A hierarchical measurement operator is a composition of block and mixing operations. It notably contains Kronecker products as a special case. Results on their hierarchical restricted isometry property (HiRIP) are derived, generalizing prior work on the recovery of hierarchically sparse signals from Kronecker-structured linear measurements. Specifically, these results show that recovery properties of the block and mixing part can be traded against each other. The measurement structure is motivated by a massive random access channel design in communication engineering. Numerical evaluation of user detection rates demonstrate benefits of the theoretical framework.


Block detection

Hierarchically sparse signals

Internet of Things (IoT)


Structured compressed sensing


Benedikt Groß

Freie Universität Berlin

Axel Flinth

Computer vision and medical image analysis

Ingo Roth

Freie Universität Berlin

Jens Eisert

Freie Universität Berlin

Gerhard Wunder

Freie Universität Berlin

2021 IEEE Statistical Signal Processing Workshop (SSP)

2693-3551 (ISSN)


2021 IEEE Statistical Signal Processing Workshop (SSP)
Rio de Janeiro/Virtual, Brazil,

Subject Categories


Other Engineering and Technologies not elsewhere specified

Signal Processing



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1/5/2022 1