A new class of measurement operators for structured compressed sensing problems, termed `hierarchical ' measurement operators, is introduced. Standard Kronecker measurement operators are block-oriented treating each block equally whereas the hierarchical measurement operator allows for processing each block with a different matrix, e.g. mixtures of FFT and Gaussian matrices of different column space size and different pilot frequencies each, which are received over multiple antennas. We prove that such hierarchical measurement operators exhibit a hierarchical RIP (HiRIP) property provided the involved matriceshave a suitable standard RIP, implying recovery guarantees for a class of algorithm involving hierarchical thresholding operations. Thereby, we generalize prior work on the recovery of hierarchically sparse signals from Kronecker-structured linear measurements. This structure arises in a variety of communication scenariosin the context of massive internet of things. We numerical demonstrate that the fast and scalable HiHTP algorithm is  suitable for solving these types of problems and evaluate its performance in terms of sparse signal recovery and block detection capability.
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.
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is introduced. Standard Kronecker measurement operators are block-oriented treating each block equally whereas the hierarchical measurement operator allows for processing each block with a different matrix, e.g. mixtures of FFT and Gaussian matrices of different column space size and different pilot frequencies each, which are received over multiple antennas. We prove that such hierarchical measurement operators exhibit a hierarchical RIP (HiRIP) property provided the involved matriceshave a suitable standard RIP, implying recovery guarantees for a class of algorithm involving hierarchical thresholding operations. Thereby, we generalize
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
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the recovery of hierarchically sparse signals from Kronecker-structured linear measurements. This structure arises in a variety of communication scenariosin the context of massive internet of things. We numerical demonstrate that the
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evaluate its performance
its performance is evaluated numerically