一阶实值多项式相位信号快速稀疏分解算法

doi:10.11772/j.issn.1001-9081.2014.06.1604

计算机应用 ›› 2014, Vol. 34 ›› Issue (6): 1604-1607.DOI: 10.11772/j.issn.1001-9081.2014.06.1604

一阶实值多项式相位信号快速稀疏分解算法

欧国建¹,²,王伟强²,蒋清平¹

1. 飞行器测控与通信教育部重点实验室(重庆大学),重庆 400044
2. 重庆电子工程职业学院软件学院,重庆 401331

收稿日期:2013-12-10 修回日期:2014-02-26 出版日期:2014-06-01 发布日期:2014-07-02
通讯作者: 欧国建
作者简介:欧国建(1975-),男,重庆人,中级实验师,博士研究生,主要研究方向:非平稳信号处理、参数估计、稀疏分解;李法平(1980-),男, 重庆人,副教授,主要研究方向: 普适计算、压缩感知;蒋清平(1976-),男,重庆人,讲师,博士,主要研究方向:压缩感知、循环谱信号处理。
基金资助:
国家自然科学基金资助项目;中央高校基本科研业务费专项资金资助项目

Fast algorithm for sparse decomposition of real first-order polynomial phase signal based on group testing

OU Guojian¹,²,WANG Weiqiang¹,JIANG Qingping²

1. College of Software, Chongqing College of Electronic Engineering, Chongqing 400044, China;
2. Key Laboratory of Aerocraft Tracking Telemetering and Command and Communication,

Received:2013-12-10 Revised:2014-02-26 Online:2014-06-01 Published:2014-07-02
Contact: OU Guojian

摘要/Abstract

摘要：

针对稀疏分解运算量巨大的问题,提出了一种针对一阶实值多项式相位信号(PPS)运算量较小的稀疏分解算法,从而实现了稀疏分解的快速性。该算法采用如下策略：首先采用级联字典的方式,即字典D由Df和Dp级联而成,其中字典Df的原子主要考虑一阶实值多项式相位信号的频率成分,不考虑相位因素,而字典Dp的原子主要考虑一阶实值多项式相位信号的相位成分,不考虑频率因素;其次对字典Df的原子与信号进行匹配测试,测试采用群测试算法搜索匹配的原子,并采用二次测试的方法来达到测试的准确性;最后根据测得的匹配频率原子,构造字典Dp,并通过匹配追踪（MP）算法搜索到匹配的相位原子,从而完成了信号的稀疏分解。仿真结果表明该算法的效率约为匹配追踪算法的604倍和遗传算法的139倍,具有运算量小、稀疏分解快的特点,复杂度仅为O(N),而且不具有智能计算的随机性。

Abstract:

Concerning the huge calculation of sparse decomposition, a fast sparse decomposition algorithm with low computation complexity was proposed for first-order Polynomial Phase Signals (PPS). In this algorithm, firstly,two concatenate dictionaries including Df and Dp were constructed, and the atoms in the Df were constructed by the frequency, and the atoms in the Dp were constructed by the phase.Secondly, for the dictionary Df, the group testing was used to search the atoms that matched the signal, and the correlation values of the atoms and the signal were tested twice to achieve the reliability. Finally, according to the matching frequency atoms tested by group testing, the dictionary Dp was constructed, and the matching phase atoms were searched by Matching Pursuit (MP) algorithm. Therefore, the sparse decomposition of real first-order PPS was finished. The simulation results show that the computational efficiency of the proposed algorithm is about 604 times as high as that of matching pursuit and about 139 times as high as that of genetic algorithm, hence the presented algorithm has less computation complexity, and can finish sparse decomposition fast. The complexity of the algorithm is only O(N).

中图分类号:

TP399

欧国建王伟强蒋清平. 一阶实值多项式相位信号快速稀疏分解算法[J]. 计算机应用, 2014, 34(6): 1604-1607.

OU Guojian WANG Weiqiang JIANG Qingping. Fast algorithm for sparse decomposition of real first-order polynomial phase signal based on group testing[J]. Journal of Computer Applications, 2014, 34(6): 1604-1607.

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一阶实值多项式相位信号快速稀疏分解算法

Fast algorithm for sparse decomposition of real first-order polynomial phase signal based on group testing

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