基于行列式和稀疏性约束的NMF的欠定盲分离方法

摘要

The decomposed left matrix of Non-negative Matrix Factorization (NMF) is required to be full column rank,which limits of its application to Underdetermined Blind Source Separation (UBSS). To address this issue, an algorithm for UBSS based on determinant and sparsity constraint of NMF, named DSNMF, was proposed in this paper. On the basis of standard NMF, determinant criterion was used for constraining the left matrix of NMF, while sparsity was used for constraining the right one. In this way, the reconstruction error, the uniqueness of mixing matrix and the spasity of original sources can be equipoised, which leads to the underdetermined blind separation of mixing matrix and original sources. The simulation results show that DSNMF both works well for good and poor sparsity of sources separation.%非负矩阵分解(NMF)要求分解得到的左矩阵为列满秩,这限制了它在欠定盲分离(UBSS)中的应用.针对此问题,提出基于带行列式和稀疏性约束的NMF的欠定盲分离算法--DSNMF.该算法在基本NMF的基础上,对NMF得到的左矩阵进行行列式准则约束,对右矩阵进行稀疏性约束.平衡了重构误差、混合矩阵的唯一性以及分离信号的稀疏特性,实现了对混合矩阵和源信号的欠定盲分离.仿真结果表明,在源信号稀疏性较好和较差两种情况下,DSNMF都能取得良好的分离效果.