计算机工程

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基于投影梯度的非负矩阵分解盲信号分离算法

李煜,何世钧   

  1. (上海海洋大学信息学院,上海 201306)
  • 收稿日期:2015-03-18 出版日期:2016-02-15 发布日期:2016-01-29
  • 作者简介:李煜(1989-),男,硕士研究生,主研方向为信号处理;何世钧(通讯作者),教授、博士后。
  • 基金项目:
    上海市科委科研计划基金资助项目(10510502800)。

Blind Signal Separation Algorithm for Non-negative Matrix Factorization Based on Projected Gradient

LI Yu,HE Shijun   

  1. (College of Information,Shanghai Ocean University,Shanghai 201306,China)
  • Received:2015-03-18 Online:2016-02-15 Published:2016-01-29

摘要: 在盲信号分离过程中,基于乘性迭代的非负矩阵分解(NMF)存在运算量大、收敛速度慢等问题。为此,在投影梯度法的基础上提出一种新的NMF盲信号分离算法。通过增加行列式约束、稀疏度约束和相关性约束条件,将最优化问题转化为交替的最小二乘问题,将投影梯度法应用于基于约束的NMF盲信号分离过程。仿真结果表明,该算法能减小重构误差,在维持源分离信号稀疏性的基础上实现混合信号的唯一分解。与经典NMF算法和NMFDSC算法相比,其收敛和分解速度更快,重构信号的信噪比更高。

关键词: 盲信号分离, 非负矩阵分解, 乘性迭代, 交替最小二乘法, 投影梯度

Abstract: In blind signal separation process,the Non-negative Matrix Factorization(NMF) based on multiplicative iteration has the problem of large computation and slow decomposition speed.So a new blind signal separation algorithm for NMF based on projected gradient method is proposed.The problem is transformed into solving alternating least squares problem by adding the determinant constraint,sparse constraint and correlation constraint,by using the projected gradient method to solve blind signal separation problems.Simulation result shows that this algorithm can reduce reconstruction error,and ensure the separation of signal sparse in realization of mixed signal only on the basis of decomposition.Compared with the classical NMF algorithm and NMFDSC algorithm,it converges faster and decomposes more quickly,and the Signal Noise Ratio(SNR) of reconstructed signal is also higher.

Key words: blind signal separation, Non-negative Matrix Factorization(NMF), multiplicative iteration, Alternating Least-squares(ALS) method, projected gradient

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