一种基于复合混沌映射的压缩感知测量矩阵构造方法研究

doi:10.3969/j.issn.0372-2112.2017.09.018

电子学报 ›› 2017, Vol. 45 ›› Issue (9): 2177-2183.DOI: 10.3969/j.issn.0372-2112.2017.09.018

一种基于复合混沌映射的压缩感知测量矩阵构造方法研究

周伟¹, 景博¹, 张航², 黄以锋¹, 李娟¹

1. 空军工程大学航空航天工程学院, 陕西西安 710038;
2. 北京机电工程研究所, 北京 100074

收稿日期:2015-05-28 修回日期:2015-11-17 出版日期:2017-09-25
- 作者简介:
- 周伟,男,1984年生于陕西西安,空军工程大学博士研究生,主要研究方向为现代检测与传感网络技术,压缩感知,故障诊断.E-mail:zwz-kgy@139.com;景博,女,1965年生于河北邯郸,空军工程大学教授,主要研究方向为故障预测与健康管理,可测试性设计,传感器网络,数据融合.E-mail:jingbo_sensor@163.com;张航,男,1990年生于陕西西安,北京机电工程研究所助理工程师,主要研究方向为人工智能、机器学习、图像信息融合.E-mail:zhh0993@163.com;黄以锋,男,1982年生于湖南耒阳,空军工程大学讲师,主要研究方向为现代检测与传感网络技术,可测试性设计,故障诊断.E-mail:huangyiff@126.com;李娟,女,1981年生于山西长治,空军工程大学博士研究生,主要研究方向为故障预测与健康管理.E-mail:daidaiquanquan123@126.com

Construction of Measurement Matrix in Compressive Sensing Based on Composite Chaotic Mapping

ZHOU Wei¹, JING Bo¹, ZHANG Hang², HUANG Yi-feng¹, LI Juan¹

1. School of Aeronautic & Astronautic Engineering, Air Force Engineering University, Xi'an, Shaanxi 710038, China;
2. Beijing Research Institute of Mechanical and Electrical Engineering, Beijing 100074, China

Received:2015-05-28 Revised:2015-11-17 Online:2017-09-25 Published:2017-09-25

摘要/Abstract

摘要： 针对常用随机测量矩阵存在硬件实现困难的不足，提出一种基于复合混沌映射的压缩感知确定性测量矩阵构造方法.首先基于Logistic映射和Tent映射构造随机性和初值敏感性更强的复合混沌映射，然后将复合混沌迭代序列经大间隔采样后进行线性变换得到的结果作为拟构造测量矩阵中的元素，并从理论上证明了该矩阵元素具有非常低的相关性.同时理论证明了所构造复合混沌测量矩阵能以高概率满足压缩感知约束等距性.实验结果表明，所构造复合混沌测量矩阵的性能优于Toeplitz测量矩阵及Logistic映射测量矩阵，与高斯随机测量矩阵的性能相仿.

关键词: 压缩感知, 测量矩阵, 混沌映射, 约束等距性

Abstract: Aiming at the difficult in hardware realization of random measurement matrix,we construct a deterministic measurement matrix based on composite chaotic mapping.The composite chaotic mapping that based on Tent mapping and Logistic mapping,has stronger randomicity and initial value sensitivity.Sampled the composite chaotic mapping sequence with large distance,and then do linear transformation to the sampling sequence.Finally,we construct the measurement matrix with the linear transformation result.We prove that the measurement matrix elements have enough statistically independent,and the measurement matrix can satisfies restricted isometry property (RIP) with large probability.The simulation result shows that our matrix has the similar performance to Gaussian random matrix,and better than Toeplitz deterministic measurement matrix and Logistic deterministic measurement matrix.

Key words: compressive sensing (CS), measurement matrix, chaotic mapping, restricted isometry property

中图分类号:

TP212.9

周伟, 景博, 张航, 等. 一种基于复合混沌映射的压缩感知测量矩阵构造方法研究[J]. 电子学报, 2017, 45(9): 2177-2183.

ZHOU Wei, JING Bo, ZHANG Hang, et al. Construction of Measurement Matrix in Compressive Sensing Based on Composite Chaotic Mapping[J]. Acta Electronica Sinica, 2017, 45(9): 2177-2183.

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一种基于复合混沌映射的压缩感知测量矩阵构造方法研究

Construction of Measurement Matrix in Compressive Sensing Based on Composite Chaotic Mapping

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