Abstract: There are two nonlinearities（hyperbolic tangent “tanh” and Gaussian function “gauss”） in the Fast-ICA algorithm to separate super-Gaussian sources. For large-scale source signals, however, these two functions are not optimal owing to high computational cost. In order to solve this problem, this paper proposes two novel rational polynomial functions to replace the original nonlinearities. Because the rational functions can be quickly evaluated, when they are used in the Fast-ICA, the computational load of the algorithm can be effectively reduced. The simulation results show that the Fast-ICA algorithms with rational nonlinearities not only can speed up the convergence but also improve the separation performance of super-Gaussian blind source separation.

Key words: Blind Source Separation（BSS）, Independent Component Analysis（ICA）, Fast-ICA, rational nonlinearity, Tchebyshev-Pade approximant

摘要： 利用Fast-ICA算法进行超高斯信源盲分离时，计算其目标函数所选取的非线性函数主要是双曲正切函数（tanh）和高斯函数（gauss）。由于tanh和gauss函数的计算负担较大，从而增加了分离混合信号的运行时间。为了提高Fast-ICA算法的收敛速度，提出两个有理非线性函数用于代替tanh和gauss，使得改进的Fast-ICA算法在提高计算速度的同时保持或提高信号的分离性能。仿真实验验证了改进算法的有效性。

关键词: 盲源分离（BSS）, 独立分量分析（ICA）, 快速独立分量分析（Fast-ICA）, 有理非线性函数, 切比雪夫-帕德逼近