基于分圆类构造卷积压缩感知测量矩阵

李玉博; 张景景; 韩承桓; 彭秀平

doi:10.11999/JEIT190878

基于分圆类构造卷积压缩感知测量矩阵

doi: 10.11999/JEIT190878

燕山大学信息科学与工程学院秦皇岛 066004

基金项目: 国家自然科学基金(61671402, 61501395)，河北省自然科学基金(F2020203043)，河北省高等学校青年拔尖人才计划基金(BJ2018018)

详细信息

作者简介:
李玉博：男，1985年生，副教授，硕士生导师，研究方向为压缩感知技术、序列设计与编码理论

张景景：女，1995年生，硕士生，主要研究方向为压缩感知技术

韩承桓：男，1995年生，硕士生，主要研究方向为压缩感知技术

彭秀平：女，1984年生，副教授，硕士生导师，研究方向为编码理论、信号设计

通讯作者:
李玉博　liyubo6316@ysu.edu.cn

中图分类号: TN911.7
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- 被引次数: 8
出版历程
- 收稿日期: 2019-11-04
- 修回日期: 2020-07-15
- 网络出版日期: 2020-12-09
- 刊出日期: 2021-02-23

Construction of Convolution Compressed Sensing Measurement Matrices Based on Cyclotomic Classes

School of Information Science & Engineering, Yanshan University, Qinhuangdao 066004, China

Funds: The National Natural Science Foundation of China (61671402, 61501395), The Natural Science Foundation of Hebei Province (F2020203043), The Fundation of Top Young Talents Program in Colleges and Universities of Hebei Province (BJ2018018)

摘要

摘要:
卷积压缩感知是近年来兴起的新型压缩感知技术。卷积压缩感知选用循环矩阵作为测量矩阵，其采样可以简化为卷积的过程，因此大大降低算法复杂度。该文基于分圆类构造适用于卷积压缩感知的测量矩阵，测量值通过利用确定性序列循环卷积信号，然后进行随机2次采样获得。该文构造的测量矩阵的相关性小于已有文献构造的测量矩阵的相关性。模拟仿真结果表明，该文构造的测量矩阵与同等条件下的随机高斯矩阵相比，可以更好地恢复稀疏信号；所构造的矩阵还可以应用于信道估计以及2维图像的重构。
- 信号处理 /
- 压缩感知 /
- 卷积 /
- 分圆类 /
- 随机采样
Abstract:
Convolutional compressed sensing emerging in recent years is a new type of compressed sensing technology. By using cyclic matrix as measurement matrices, the sampling in convolutional compressed sensing can be simplified into convolution process, thus the complexity of the algorithm is greatly reduced. In this paper, a construction of measurement matrices for convolutional compressed sensing based on cyclotomic classes is proposed. The measurements are obtained by using the circulate convolution signal of the deterministic sequence and then by random subsampling. The correlation of the measurement matrix constructed in this paper is smaller than that of the existing constructions in the literature. The simulation results show that the measurement matrix constructed in this paper can recover the sparse signal better than the random Gaussian matrix under the same conditions. The proposed matrix can also be applied to channel estimation and reconstruction of two-dimensional images.
- Signal processing /
- Compressed sensing /
- Convolution /
- Cyclotomic class /
- Random sampling

HTML全文

图 1 相关性分布图

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图 2 不同稀疏度下的重构百分比

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图 3 不同稀疏度下的重构百分比

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图 4 不同稀疏度下的输出信噪比

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图 5 不同稀疏度下的输出信噪比

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图 6 不同测量矩阵重构2维图像

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图 7 信道脉冲响应的实值及其估计

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图 8 均方误差性能与组合多路径数

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表 1 与已有序列构造的矩阵相关性比较

	对角向量 $\sigma$	序列长度 $N$	相关性参数 $\mu ({{A}})$
文献[10]	抽样Sidelnikov序列	$N = \dfrac{ { {p^m} - 1} }{c}$ , $c$ 为偶数	$\sqrt {c + {{\rm{1}} / N}} + {1 / {\sqrt N }}$ , $N$ 为偶数
文献[10]	抽样Sidelnikov序列	$N = \dfrac{ { {p^m} - 1} }{c}$ , $c$ 为偶数	$\sqrt {c + {1 / N}}$ , $N$ 为奇数
文献[11]	Extended Frank-Zadoff-Chu(扩展FZC)序列	$N$ 为偶数	$4 + {4 / {\sqrt N }}$
	Extended Frank-Zadoff-Chu(扩展FZC)序列	$N$ 为奇数	$2.69 + {{8.15} / {\sqrt N }}$
	Extended Golay(扩展Golay)序列	$N = {2^{{k_1}}}{10^{{k_2}}}{26^{{k_3}}}$ , $N$ 为偶数， ${k_1},{k_2},{k_3}$ 为整数	$2 + {2 / {\sqrt N }}$
	Extended Golay(扩展Golay)序列	$N = {2^{{k_1}}}{10^{{k_2}}}{26^{{k_3}}} \pm 1$ , $N$ 为奇数， ${k_1},{k_2},{k_3}$ 为整数	$2 + {1 / {\sqrt N }}$
本文	由2阶分圆类得到的序列	$N = p$ 为奇素数， $p \equiv 1({\rm{mod}}4)$	$1 + {1 / {\sqrt N }}$
本文	由 $e > 2$ 阶分圆类得到的序列	$N = p$ 为奇素数	$\mu ({{A} }) \le 2$

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