Blind Separation Of Mixed Audio Signals Based On Improved FastICA

Blind source separation(BSS) has become a hot research topic in signal processing field recently, the aim of BSS is to estimate the source signals that is unknown only by the observed signals that are represented by a set of time-series or parallel signals. Typical examples of BSS include RF interference signals of mobile phone, brain wave signals collected by sensor, mixed audio signals recorded by microphone and so on. Independent Component Analysis(ICA) is an effective method to deal with the BSS problem, which has gained widespread concern on the development of BSS. The principle of ICA method is to estimate the demixing matrix through an appropriate objective function optimized by a selected iterative algorithm, by which the observed signals are able to be linearly transformed to the approximation of the source signals.This paper introduces the history and millstones of the ICA research based on the background of BBS. Through the analysis of the basic principle of ICA, the uncertainty and constraints of the ICA model can be summarized as: the study only applies to independent source signals which obey non-gaussian distribution. According to the priciple of ICA, this paper highlights several classical objective functions and iterative algorithms of the ICA model. Among the preliminary process of the ICA model, centering and whitening the signals are necessary for the simplicity of the estimation which can be theoretically proved.FastICA is one of the most commonly used algorithm in ICA model. Depending on the measuring methods of non-Gaussianity in it, two types of FastICA algorithm are introduced in details, which are FastICA based on kurtosis and FastICA based on negentropy. And through analysis of the principle of these two algorithms and their inherent defects, corresponding improved methods are proposed in this paper. For FastICA based on Kurtosis, it is proposed that the original algorithm can be improved by the conjugate gradient method so as to avoid the convergence instability problem. According to the simulation, improved algorithm not only solve the convergence problem but also performs a better separation result. For FastICA based on negentropy, firstly, the steepest descent method is proposed to overcome the sensitive initial values problem, sencondly, the secant method is introduced to reduce the algorithm complexity. The simulation result shows that the solution proposed by this paper is valid. Finally, by comparing the two improved algorithms, both algorithms have their advantages, the improved FastICA based on kurtosis performs a better separation results, while the improved FastICA based on nengentropy has a faster convergence speed. After balanced consideration, the latter improved algorithm was considered more practical.