一种基于L1稀疏正则化和非负矩阵分解的盲源信号分离新算法

doi:10.3969/j.issn.1001-2400.2010.05.011

J4 ›› 2010, Vol. 37 ›› Issue (5): 835-841.doi: 10.3969/j.issn.1001-2400.2010.05.011

一种基于L₁稀疏正则化和非负矩阵分解的盲源信号分离新算法

殷海青;刘红卫

(西安电子科技大学理学院，陕西西安 710071)

收稿日期:2009-10-09 出版日期:2010-10-20 发布日期:2010-10-11
通讯作者: 殷海青
作者简介:殷海青(1977-)，男，西安电子科技大学博士研究生，E-mail: yinhaiqing2008@163.com．
基金资助:
国家自然科学基金资助项目(60603098,61072144);2009年度西安电子科技大学基本科研业务费资助项目(JY10000970004)

New blind source separation algorithm based on L₁ sparse regularization and nonnegative matrix factorization

YIN Hai-qing;LIU Hong-wei

(School of Science, Xidian Univ., Xi'an 710071， China)

Received:2009-10-09 Online:2010-10-20 Published:2010-10-11
Contact: YIN Hai-qing

摘要/Abstract

摘要：

针对线性混合模型下的盲源分离这一反问题，提出了一种结合迭代正则化和非负矩阵分解的交替最小化算法．首先把该问题转化为有界约束的二次规划，然后采用了一种自适应BB(Barzilai-Borwein)步长的投影梯度算法来求解．该方法不仅可减少存储量，提高算法速度，而且还很好地刻画了信号的稀疏性和独立性．理论分析和数值试验都验证了该方法的有效性，对混合的二维图像能提高分离的信干比．

关键词: 盲源信号分离, 反问题, 非负矩阵分解, 投影梯度算法, 信干比

Abstract:

For the inverse problem of blind source separation (BSS)， with which sources are mixed linearly, an alternating minimization algorithm based on iterative regularization and nonnegative matrix factorization(NMF) is proposed. Firstly, this problem is transformed into a bound constrained convex quadratic problem, and then a gradient projection algorithm with adaptive Barzilai-Borwein steplength selection rules is used. This method not only requires lower storage, and improves the speed of computing but also can explain the signals' sparsity and independence appropriately. Theoretical analysis and experimental results show that he new method is promising. The signal-to-Interference Ratio (SIR) can be improved for the mixed two dimensional images.

Key words: blind source separation (BSS), inverse problem, nonnegative matrix factorization(NMF), gradient projection algorithm, signal-to-interference ratio (SIR)

殷海青;刘红卫. 一种基于L₁稀疏正则化和非负矩阵分解的盲源信号分离新算法[J]. J4, 2010, 37(5): 835-841.

YIN Hai-qing;LIU Hong-wei. New blind source separation algorithm based on L₁ sparse regularization and nonnegative matrix factorization[J]. J4, 2010, 37(5): 835-841.

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一种基于L₁稀疏正则化和非负矩阵分解的盲源信号分离新算法

New blind source separation algorithm based on L₁ sparse regularization and nonnegative matrix factorization

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