  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.
