Hierarchical isometry properties of hierarchical measurements

A new class of measurement operators, coined hierarchical and prove results guaranteeing the efficient, stable robust recovery hierarchically structured signals from such measurements. We derive bounds on their restricted isometry properties based constants constituent matrices, generalizing extending prior work Kronecker-product As an exemplary application, we apply theory to two communication scenarios. The fast scalable HiHTP algorithm is shown be suitable for solving these types problems its performance evaluated numerically in terms sparse signal block detection capability.