分层测量的分层等距性质
信息论
2022-02-16 v4 数值分析
math.IT
数值分析
摘要
提出一类新的测量算子, 称为分层测量算子, 并证明可保证由此类测量中高效、稳定且鲁棒地恢复分层结构信号的结论。我们基于其组成矩阵的受限等距常数推导其分层受限等距性质的界, 推广并扩展了先前关于 Kronecker 积测量的工作。作为一个示例应用, 我们将该理论应用于两种通信场景。表明快速且可扩展的 HiHTP 算法适用于求解此类问题, 并从稀疏信号恢复与块检测能力方面对其性能进行数值评估。
引用
@article{arxiv.2005.10379,
title = {Hierarchical Isometry Properties of Hierarchical Measurements},
author = {Axel Flinth and Benedikt Groß and Ingo Roth and Jens Eisert and Gerhard Wunder},
journal= {arXiv preprint arXiv:2005.10379},
year = {2022}
}
备注
22 pages, 5 figures. v3: Significant rework of previous version. Section on incoherent blocks added, as well as more numerical experiments. v4: Revision of the manuscript. Several previous mistakes have been corrected