基于时间序列变分贝叶斯理论的信号盲源分离

Signal blind source separation based on time series variational Bayesians theory

研究信号盲源分离中源信号和混合矩阵估计问题。独立分量分析盲源分离的不足之处在于不能估计混合矩阵和源信号的能量及顺序;变分独立因子分析盲源分离的不足之处在于依赖参数初值。将一般变分贝叶斯理论用于时间序列,推导出时间序列的变分贝叶斯期望极大算法。将此算法用于信号盲源分离,同时将传感器噪声逆方差的分布取为Wishart分布,得到了理论上更合理的后验分布参数更新规则。仿真数据和实际语音信号盲源分离结果表明这种方法可以比较准确地估计混合矩阵和源信号,在一定程度上弥补了独立分量分析和变分独立因子分析盲源分离的不足。

We study the issue of estimating the source signal and the mixing matrix in blind source separation of the signals. The deficiency of the blind source separation through independent component analysis is that it can not estimate the energies and orders of the mixing matrix and the source signals, whereas the deficiency of the blind source separation based on variational independent factor analysis is its strong dependence on initial parameters. Here, the general variational Bayesians theory is applied to the time series, and a novel variational Bayesian expectation-maximization algorithm for the time series is deduced accordingly. Moreover, the proposed method is applied to the blind source separation of the signals, and then more reasonable rules to update posterior parameters are deduced, where the distribution of the inverse variance of the sensor noises is assumed as Wishart distribution. The proposed algorithm was applied to the sources of simulation signals and real speech signals, the results show that the adopted method can accurately estimate the mixing matrix and the source signals, and it can reduce the deficiency of the independent component analysis and the independent variational factor analysis to a certain degree.