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.

翻译：新的测量操作员类别,创下等级测量操作员,并证明能够保证从这类测量中有效、稳定和有力地恢复分级结构信号。我们根据其组成矩阵的有限等量定常数,得出其等级限制的异度特性的界限,对克罗内尔产品测量的先前工作加以概括和扩展。我们作为示范应用,将理论应用于两种通信情景。快速和可缩放的HHHTP算法被证明适合于解决这类问题,其性能从微小信号恢复和阻塞探测能力的角度进行了数字评估。