基于约束NMF的欠定盲信号分离算法*

提出一种约束非负矩阵分解方法用于解决欠定盲信号分离问题。非负矩阵分解直接用于求解欠定盲信号分离时，分解结果不唯一，无法正确分离源信号。本文在基本非负矩阵分解算法基础上，对分解得到的混合矩阵施加行列式约束，保证分解结果的唯一性；对分解得到的源信号同时施加稀疏性约束和最小相关约束，实现混合信号的唯一分解，提高源信号分离性能。仿真实验证明了本文算法的有效性。

Algorithm for underdetermined blind signal separation based on constrained NMF

A constrained nonnegative matrix factorization (NMF) method is proposed to resolve the problem of underdetermined blind signal separation in this paper. It is hard to obtain unique factorization and correctly separate source signals when NMF is directly applied to resolve problem above. In this paper, on the basis of standard NMF, determinant criterion was imposed on estimated mixing matrix to achieve the unique factorization of NMF; sparsity and the least correlated component constraints was imposed on estimated sources to realize the unique separation of mixed signals and improve the performance of source separation. Simulation results show effectiveness of the proposed algorithm.