The Research Of Noisy Blind Source Separation Based On Independent Component Analysis And Shrinkage Denoising

Under the situation that both the transmit channel and sources are unknown,only depending on the observation data received by sensors to resume the source signals is called Blind Source Separation(BSS).BSS has an extensive application prospect in many fields such as biomedical applications,audio signals separation and multiuser's communication.Independent Component Analysis(ICA)is a very effective tool for solving the BSS problem.Instantaneous square linear mixed model which is the simplest ICA model is researched in this paper,the uncertainty and basic supposing of ICA were also analyzed.The basic ICA method is constituted by a objective function which is derived by the measurement criterion of independent degree and an optimization algorithm which is used to solve the optimization problem given by the objective function.The FastICA al-gorithm based on maximization of nongaussianity is mainly discussed in this paper.We focus on the nonlinearities which are used in FastICA algorithm and influence the per-formance of it.Since the classical nonlinearities(tanh and gauss)are not the optimal ones due to their slow computational speed,we propose two novel rational nonlinearities that have faster computational speed and almost the same or better separation perform-ance comparing with the classical ones.As they originate from Pade approximant of tanh and gauss but the coefficients are adjusted,we name them VTP(Variant Tanh Pade)and VGP(Variant Gauss Pade)respectively.Noisy BSS/ICA,as it approaches the reality,is frequently considered in many prac-tical applications.In this paper,we mainly discuss the "sensor" noise model,adding Gaussian white noise to the music audio mixtures.To solve noisy BSS/ICA problem,we deploy denoising pre-processing before performing FastICA.Rather than traditional wavelet shrinkage denoising,we employ a more advanced shrinkage denoising algorithm,Parallel Coordinate Descent(PCD)iterative shrinkage based on sparse representations and redundant dictionary,to accomplish the denoising task.PCD iterative shrinkage de-noising has special effect and superior performance than other denoising method,but it has not attracted much attention in the noisy BSS/ICA community until now.Although it has been widely applied in image processing,but it has not been used in audio signals processing.For music audio signals,we first present denoising with PCD iterative shrinkage denoising as pre-processing under the framework of noisy BSS/ICA.From the experiment results we can know that this method is able to implement noisy BSS/lCA in audio signals.