杜昊辰,
刘琦,
童子权
哈尔滨理工大学测控技术与仪器黑龙江省高校重点实验室 ??哈尔滨 ??150080
基金项目:国家自然科学基金(61501150)，黑龙江省自然科学基金(QC2014C074)
详细信息
作者简介:盖建新：男，1980年生，博士，副教授，研究方向为压缩感知、亚奈奎斯特采样理论、频谱感知技术等
杜昊辰：男，1991年生，硕士生，研究方向为电子与通信工程
刘琦：男，1994年生，硕士生，研究方向为仪器仪表工程
童子权：男，1968年生，教授，研究方向为现代电子测量仪器与系统、信号处理等
通讯作者:盖建新 gjx800608@126.com
中图分类号:TP391计量
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被引次数:0
出版历程
收稿日期:2018-04-11
修回日期:2018-10-29
网络出版日期:2018-11-08
刊出日期:2019-02-01
Sub-Nyquist Sampling Recovery Algorithm Based on Kernel Space of the Random-compression Sampling Value Matrix
Jianxin GAI,,Haochen DU,
Qi LIU,
Ziquan TONG
The Higher Educational Key Laboratory for Measuring & Control Technology and Instrumentations of Heilongjiang Province, Harbin University of Science and Technology, Harbin 150080, China
Funds:The National Natural Science Foundation of China (61501150), The Natural Science Foundation of Heilongjiang Province (QC2014C074)
摘要
摘要:针对现有调制宽带转换器亚奈奎斯特采样重构算法性能不高问题，该文提出一种基于采样值核空间的支撑重构算法和随机压缩降秩方法，将两者结合得到一种高性能采样重构算法。首先利用随机压缩变换在不改变未知矩阵稀疏特性的前提下将采样方程转化为多个新的多测量向量问题，然后利用采样值矩阵核空间与采样矩阵支撑正交的关系获取联合稀疏支撑集，最后通过伪逆完成重构。从理论和实验两个方面对所提方法进行了分析和验证。数值实验表明，与传统重构算法相比，所提算法提高了重构成功率、降低了高概率重构所需的通道数，而且重构性能总体上随压缩次数增加而提高。
关键词:稀疏重构/
亚奈奎斯特采样/
多测量向量/
调制宽带转换器
Abstract:To solve the low performance problem of the existing Modulated Wideband Converter (MWC)-based sub-Nyquist sampling recovery algorithm, this paper proposes a support recovery algorithm based on the kernel space of sampling value and a random compression rank-reduction idea. Combining them, a high-performance sampling recovery algorithm is achieved. Firstly random compression transforms are used to convert the sampling equation into several new multiple-measurement-vector problems, without changing the sparsity of the unknown matrix. Then the orthogonal relationship between the kernel space of sampling value and the support vectors of sampling matrix is utilized to obtain joint sparse support set of the unknown. The final recovery is performed by the pseudo inversion. The proposed method is analyzed and verified by theory and experiment. Numerical experiments show that, compared with the traditional recovery algorithm, the proposal can improve the recovery success rate, and reduce the channel number required for high-probability recovery. Furthermore, in general, the recovery performance improves with the rise of compression times.
Key words:Sparse recovery/
Sub-Nyquist sampling/
Multiple measurement vectors/
Modulated Wideband Converter (MWC)
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