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

作　　者：欧国建[1,2] 李法平[1] 蒋清平[2] 

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

出　　处：《计算机应用》2014年第6期1604-1607,1665,共5页journal of Computer Applications

基　　金：国家自然科学基金资助项目(61301120);中央高校基本科研业务费专项资金资助项目(CDJZR12160020)

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。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 Of, 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）.

关 键 词：多项式信号 群测试 稀疏分解 匹配追踪 冗余字典 

分 类 号：TP399[自动化与计算机技术—计算机应用技术]