Abstract: Sparse representation of signals has been applied in signal processing.Based on the sparse matching pursuit（MP） decomposition is the most common way on signal sparse decomposition，and it is almost the fastest algorithm in all the sparse decomposition algorithms，but the computational burden in signal sparse decomposition process is very huge.A new fast algorithm is presented based on Matching pursuit（MP） signal sparse decomposition.Genetic algorithms（GA） is applied to effectively search in the dictionary of atoms for the best atom at each step of MP.An improved algorithm is presented to solve the existence of the basic genetic algorithm immature convergence and easy optimal solution in to local issues.Finally the experimental results show that the performance of the proposed algorithm is very good.

Key words: signal processing, sparse decomposition, Matching Pursuit（MP）, Genetic Algorithms（GA）, improved algorithms

摘要： 信号的稀疏表示在信号处理的许多方面有着重要的应用，基于MP的稀疏分解是目前信号稀疏分解的最常用方法，也是几乎所有稀疏分解算法中速度最快的，但其存在的关键问题仍然是计算量十分巨大。基于利用MP（Matching Pursuit）方法实现的信号稀疏分解算法，采用遗传算法（GA）快速寻找MP 过程中每一步分解的最佳原子。并针对基本遗传算法存在的未成熟收敛和易陷入局部最优解的问题，提出了对基于GA和MP的信号稀疏分解的一种改进算法，实验结果证实了改进算法的有效性。

关键词: 信号处理, 稀疏分解, 匹配跟踪（MP）, 遗传算法（GA）, 改进算法