Abstract: If there are more mixtures than source signals, the mixing matrix in the Blind Source Separation（BSS） problem is described as an over-determined matrix. As a result, the separation task can be realized through estimate the inverse of the mixing matrix directly. This paper presents a conjugate gradient based BSS method for such over-determined mixing case. The over-determined BSS cost function is first obtained based on the minimum mutual information principle combined with the singular value decomposition of the de-mixing matrix with full row rank. The conjugate gradient optimization algorithm is then exploited to deduce the training equations for the de-mixing matrix. In each of iterations, the score functions of the separation signals are estimated by a kernel probability density estimation method, avoiding the problem of many traditional BSS algorithm where the score functions should be replaced by specific nonlinear functions. The efficiency of the proposed over-determined BSS algorithm is validated by several simulations.

Key words: conjugate gradient, score functions, mutual information, over-determined mixtures

摘要： 当混合信号的个数多于源信号时，盲源分离模型中的混合矩阵被描述为一个超定矩阵，因此不能直接通过估计逆矩阵的方法来得到分离矩阵。针对该线性超定混合情况提出了一种基于共轭梯度的盲源分离方法。该方法基于最小互信息准则，通过对行满秩分离矩阵的奇异值分解而引入了超定盲源分离的代价函数。利用共轭梯度优化算法推导出了迭代计算分离矩阵的更新公式。在每次迭代计算中，利用随机变量概率密度估计的核函数法在线估计分离信号的评价函数。避免了诸多传统盲分离算法中只能凭经验选取特定的非线性函数来代替评价函数的问题。仿真结果验证了所提算法的有效性。

关键词: 共轭梯度, 评价函数, 互信息, 超定混合信号