关键词: 共轭梯度, 评价函数, 互信息, 超定混合信号

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