Computer Science and Application
Vol.4 No.11(2014), Article ID:14431,5 pages
DOI:10.12677/CSA.2014.411040

NMF Blind Source Separation Algorithm with Orthogonal Constraint

Tao Chen, Wensheng Sun, Yu Zhou, Mali Chen

School of Communication Engineering, Hangzhou Dianzi University, Hangzhou

Email: 411533714@qq.com

Received: Oct. 5th, 2014; revised: Nov. 6th, 2014; accepted: Nov. 15th, 2014

ABSTRACT

In order to enhance the performance of the Blind Source Separation Algorithm and reduce the complexity of Blind Source Separation Algorithm, NMF Blind Source Separation Algorithm with orthogonal constraint (NMF-DSO) is presented in this paper. This optimized algorithm adds orthogonal constraint to NMF objective function to optimize objective function and uses the multiplicative updated rule to get the updated formula which gets the number of multiplications each time less than NMF blind source separation algorithm with constraints (NMF-DSC). Theoretical analysis and simulations all show that the performance of the proposed method is superior to that of the NMF Blind Source Separation Algorithm with orthogonal constraint (NMF-DSC) algorithm.

Keywords:Orthogonal Constraint, Blind Source Separation, Multiplicative Update, Non-Negative Matrix Factorization

Email: 411533714@qq.com

1. 引言

2. 基于正交约束的NMF盲源分离算法

NMF的优化问题可以利用原始非负矩阵与重构的非负矩阵之间的欧式距离来度量它们之间的相似度，其目标函数可以写为：

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

3. 算法的仿真分析

3.1. 分离性能分析

Figure 1. Source signals

Figure 2. Mixed sign

3.2. 复杂度分析

(12)

Figure 3. The separated signal of NMF-DSO

Figure 4. The separated signal of NMF-DSC

Table 1. The SNR of separated signal based on two algorithms

4. 结束语

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