Super-gaussian BSS Using Fast-ICA With Rational Nonlinearities

The blind source separation(BSS)is to separate the sources from their mixtures without any prior knowledge about the mixing process or the sources.BSS is a powerful signal processing method,and has found wide applications in a variety of areas including signal processing,separating audio signals,mobile communications,biomedical systems,and seismic signal processing.As a statistical model,Independent Component Analysis(ICA)is to recover the latent components from observations.So the ICA is a very effective method for solving the BSS problem.The ICA model in general is constituted by an objective and an optimization algorithm.The FastICA algorithm based on maximization of nongaussianity is selected as the optimization algorithm in this paper.There are two nonlinearities(hyperbolic tangent ’tanh’ and Gaussian function ’gauss’)in the FastICA 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.The simulation results show that the Fast-ICA algorithms with rational nonlinearities not only can have faster computational speed but also have almost the same or better separation performance.As they originate from Tchebyshev-Pade approximant of tanh and gauss,we named them VTT(Variant Tanh Tchebyshev-Pade)and VGT(Variant Gauss Tchebyshev-Pade)respectively.However,in real life,there is always some kind of noise present in the observations.So we must consider how to remove the noise effectively.In this paper,we mainly discuss the "sensor" noise model,adding Gaussian white noise to the audio mixtures.Aiming at the noise model,the mixtures can be denoised before the Fast-ICA.Wavelet threshold de-noising,one of the wavelet de-noising methods,is an effective tool for remove noise in signal processing.In this paper,the characteristics of the wavelet threshold de-noising is analyzed and a new thresholding function is proposed.This new thresholding function has many advantages over classical soft-and hard-thresholding function.It is as continuous as the soft-thresholding function,and has a high order derivative.The simulation results show that the new method gives better MSE performance and SNR gains than hard-and soft-thresholding methods.Besides,the denoised signals using the new function also follow the original signal very closely.