源数估计对于独立分量分析算法的影响分析

Influence of Source Number Estimation on Independent Component Analysis Method

研究了源数估计对于独立分量分析算法的影响。对于正定模型,当估计源数少于真实源数时,模型变为超定模型,采用自然梯度法开展仿真实验;当估计源数多于真实源数时,模型变为欠定模型,采用基于时频单源点检测的混合矩阵估计算法和子空间表示信号恢复算法开展仿真实验。实验结果表明,在满足一定信噪比的条件下,对于正定模型超定化问题,通常有数目等于估计源数的源信号能够成功分离;对于正定模型欠定化问题,通常所有源信号都能正确分离,只是分离信号中出现了1个或多个源信号的拷贝,可以通过检测分离信号的相关性,对拷贝信号进行剔除或合并,对分离效果无影响。研究结论对于独立分量分析算法的应用具有一定参考价值。

The influence of source number estimation on application of Independent Component Analysis （ICA） methods is researched. For positive model of ICA, when the estimated source number is less than the actual source number, the positive model is changed to over-determined model, and natural gradient algorithm is implied for simulation experiment. To the case that the estimated source number is more than the actual source number, the positive model is changed to under-determined model, for which the hybrid matrix estimation algorithm based on single source detection is used for estimating the hybrid matrix, and subspace representation algorithm is employed for studying the influence on source separation. Experimental results show that, as to the problem of positive model changing to over-determined model, in the case of signal to noise ratio satisfying the requirements, the number of successfully separated source signals is usually equal to that of estimated source number. As to positive model changing to under-determined model, usually all of the source signals can be successfully separated, but there is one or more of the separated signals is the copy of the original source signal. In this case, the separated signals can be merged based on correlation analysis, and all of the original source signals can be separated successfully. The results supply a referenced for applying ICA methods.