联合过完备库下的信号稀疏分解  

Sparse decomposition over combined over-complete dictionary

作　　者：余付平[1] 冯有前[2] 高大化[2] 安芹力[2] 

机构地区：[1]空军工程大学导弹学院,陕两三原7138001 [2]空军工程大学理学院,西安710051

出　　处：《控制与决策》2012年第8期1237-1240,1245,共5页Control and Decision

基　　金：国家自然科学基金项目(61003148);陕西省自然科学基础研究计划项目(SJ08F10)

摘　　要：针对具有多个特征成分的复合信号在单一特征过完备库下无法实现稀疏分解的问题,提出构建联合过完备库的思想.联合过完备库由多个具有单一特征的过完备库联合构成,包含复合信号中各分量信号的信息,使得复合信号在其上具有稀疏性.利用稀疏分解算法,对多个复合信号在相应的联合过完备库上进行稀疏分解和信号重构,并与单一特征过完备库的分解结果进行了对比分析.仿真结果表明了构建联合过完备库思想的合理性和有效性.Complex signal with multiple features can not be decomposed sparsely in single feature over-complete dictionary, so the idea of building the combined over-complete dictionary is proposed. The combined over-complete dictionary is composed of many over-complete dictionaries with a single feature, and contains the information of every separate signal. The complex signal has sparsity in the combined over-complete dictionary. The decomposition result of the complex signal in a combined over-complete dictionary is contrasted with the decomposition result in an over-complete dictionary with a single feature. Simulation results show the rationality and effectiveness of the proposed idea of the combined over-complete dictionary.

关 键 词：联合过完备库 稀疏分解 复合信号 信号重构 分解系数 

分 类 号：TN957.51[电子电信—信号与信息处理]