论文标题
分层测量的层次等轴测特性
Hierarchical Isometry Properties of Hierarchical Measurements
论文作者
论文摘要
一类新的测量运算符，创建的分层测量运算符，并证明结果可以保证从此类测量值中效率，稳定和稳健的层次结构信号恢复。我们基于其组成矩阵的限制等轴测常数，在其层次限制的等轴测特性上得出边界，从而概括并扩展了对Kronecker-rododuct量的测量。作为模范应用，我们将理论应用于两个通信方案。快速可扩展的HIHTP算法被证明适用于解决这些类型的问题，其性能是根据稀疏信号恢复和阻止检测能力来数字评估的。
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.
