基于ICA的盲信号分离正定性检验方法

 盲信号分离中,判断观测信号个数与实际信源个数的关系对于信号分离算法的选择和算法效果的评估非常重要,但目前还缺乏有效的方法对正定和欠定情况进行区分性检验.针对这一问题,本文提出两种检验方法.第一种方法通过分析整个数据序列ICA分解输出分量之间的独立性来实现.理论分析表明,欠定条件下ICA分解输出分量之间必然不具有独立性,而正定条件下,只要源信号满足独立的前提假设,ICA分解输出分量之间可以相互独立.第二种方法中,我们对数据序列不同位置添加等长时间窗,根据ICA分解基向量的稳定性来检验正定性.理论分析表明,正定条件下不同窗口数据ICA分解的基向量都收敛到混合阵的基向量上,而欠定条件下,分解得到的基向量随不同时窗内源信号分布的变化而改变.本文通过仿真实验,证明了这两种方法的可行性.

Approaches for Checking Determinnancy in ICA-Based BSS

In a blind signal separation problem,for the purpose of algorithm selection and results evaluation,it is important to check the determinacy of the observation matrix.To the best of our knowledge,there is no available way to tell the determined case from the underdetermined one under the condition of full rank.To overcome this problem,we propose two methods based on ICA (independent component analysis) for determinancy check.In the first approach,we check the determinancy by looking into the independency of the output signals estimated by ICA.In theory,the outputs won't be independent in the underdetermined case,while in the determined case,the outputs will be independent if the source signals are independent.In the second approach,the observation data is windowed,and different windowed signal series are acquired by shifting the center of the rectangular window.when ICA is performed on the signal series,the basis vectors which are columns of the inverse of unmixing matrix are supposed to be stable in the determined case while unstable in the underdetermined case due to the variation of source signals’ statistical distribution.Experimental results show that our methods achieved good performance.