超定盲信号分离的半参数统计方法

Semi-parametric statistical approach for overdetermined blind source separation

研究观测信号的数目m不小于源信号的数目n情况下盲信号分离问题。首先证明若混合矩阵满列秩,则在本质相等意义下,存在唯一的m×m非奇异矩阵使得分离系统的输出除零信号外,其它非零信号即是希望提取的源信号。基于此,采用半参数统计方法构造超定盲信号分离的估计函数,给出相应的学习算法;理论证明了该算法具有等变化性和分离矩阵的非奇异特性,并借助于源信号数目未知且动态变化的计算机仿真验证了其有效性。

This paper addresses the problem of overdetermined blind source separation （ODBSS）. Firstly, it is shown there exits, in the sense of essential equality, a unique m × m nonsingular de-mixing matrix, where the outputs of the separation system consist of the scaled and permuted source signals plus zero signals. Secondly, based on the semiparametric theory, an estimating function is constructed and the corresponding learning algorithms are proposed. It is proved that the proposed algorithms for ODBSS is equivariant and has the property of keeping the demixing matrix from becoming singular. Due to the uniqueness of equilibrium or separating point of the algorithms, the new algorithms converge stably. The validity and stability of the new algorithms are illustrated via the computer simulations on ODBSS with an unknown and at the same time dynamic changing number of sources.