组合正交基字典稀疏分解快速匹配追踪算法  

A quick MP algorithm of sparse decomposition by overcomplete dictionary combined by orthogonal bases

作　　者：安芹力[1] 冯有前[1] 高大化[1] 余付平[2] 

机构地区：[1]空军工程大学理学院,陕西西安710051 [2]空军工程大学导弹学院,陕西西安713800

出　　处：《电子设计工程》2011年第2期78-80,共3页Electronic Design Engineering

基　　金：陕西省自然科学基金资助项目(SJ08F10)

摘　　要：组合正交基字典稀疏分解通过正交基的级联来构造完备字典,实现稀疏分解。针对稀疏分解的常见算法计算复杂度高的问题,提出一种快速匹配追踪算法。该算法首先求出并存储正交基向量之间的内积,然后根据向量正交基展开系数为其与正交基向量内积的性质将内积运算转化为代数运算,得到一种快速匹配追踪算法。实验结果表明,基于Dirac基和DCT基构成的完备字典对信号leleccum进行稀疏分解时,与匹配追踪(MP)算法相比,该算法的计算速度提高了大约10倍。Sparse decomposition by overcomplete dictionary combined by orthogonal bases means that a signal is sparsely decomposed by overcomplete dictionary combined by orthogonal bases. For the extremely high complexity of usual algorithms for sparse decomposition, a quick MP algorithm is proposed. The algorithm adopts the idea that inner product operation is transformed to algebra operation by the properties of orthogonal base. Simulation results of the leleccum signal decomposed by overcomplete dictionary combined by Dirac base and DCT base show that the calculating speed of the algorithm in this paper increases by about ten times compared with MP＇s.

关 键 词：匹配追踪 稀疏分解 快速算法 正交基 

分 类 号：TN911.72[电子电信—通信与信息系统]