AN ADAPTIVE NONLINEAR FUNCTION CONTROLLED BY ESTIMATED OUTPUT PDF FOR BLIND SOURCE SEPARATION
Kenji Nakayama, Akihiro Hirano, Takayuki Sakai · 2003
In blind source separation, convergence and separation per-formance are highly dependent on a relation between a prob-ability density function (pdf) of the output signals y and nonlinear functions f(y) used in updating coefficients of a separation block. This relation was analyzed based on kurtosis κ4 of the output signals. The nonlinear functions, tanh(y) and y3 have been suggested for super-Gaussian (κ4 ≥ 0) and sub-Gaussian (κ4 < 0) distributions, respec-tively. Furthermore, an adaptive nonlinear function, which can be continuously controlled, was proposed. The nonlin-ear function is formed as a linear combination of y3 and tanh(y). Their linear weights are controlled by the esti-mated κ4. Although the latter can improve separation per-formance, its performance is still limited especially in dif-ficult separation problems. In this paper, a new method is proposed. Nonlinear functions are directly controlled by the estimated pdf p(y) of the separation block outputs y. p(y) is expressed by a mixture Gaussian model, whose parameters are iteratively estimated sample by sample. f(y) and p(y) are related by the stability condition f(y) = −(dp(y)/dy)/p(y). Blind source separation using 2 ∼ 5 channel music signals are simulated. The proposed method is superior to the above conventional methods. Three Gaussian functions are enough to express the output pdf. 1.