Before revision: 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.
After revision: A new class of measurement operators for structured compressed sensing problems, termed `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 the recovery of hierarchically sparse signals from Kronecker-structured linear measurements.