Study On Blind Separation Algorithm Of Speech Based On Independent Component Analysis

IntroductionBlind signal separation (BSS) can recover the original source signals bymeans of received sensor signals. BSS algorithms are only based on the statisticalcharacteristic of the source signals without priori information on either sourcesignals or mixing channels. This process can also be called independent componentanalysis (ICA), too. Since very little priori information is needed in the BSS, theBSS technique is widely applied in many areas such as communication, biomedicalengineering, image enhancement, radar systems, seismology, data mining, etc.At present, the BSS technique based on information theory is a hot researchtopic of ICA techniques. The realization of ICA depends on two aspects: theindependence criterion and the optimization algorithm. They are important to theICA and can decide the statistical characteristic and the algorithm characteristic ofthe ICA method respectively. Different independence criterions can be obtainedaccording to different separation rules such as minimum criterion of mutualinformation, maximization criterion of information, maximization criterion ofneg-entropy and maximum likelihood estimation criterion. There are alsooptimization algorithms like gradient algorithm, natural gradient algorithm,generalizations algorithm of basis natural gradient, equivariant adaptive separationalgorithm based on ICA and iteration inversion algorithm, etc.The important application of ICA to the field of speech signal processing isthe blind speech signal separation which comes of the attractive research on the"cocktail party" effect. In order to enhance an interested speech signal, the keyproblem is how to separate mixed speech signals.The instantaneous separation algorithms and convolution mixed speech signalseparation methods are all studied in this paper. A modified probability densityfunction is proposed as an estimation of the probability density function for speechsignal, which composes the separation algorithm of speech signals. The proposedfunction can improve convergent speed of the separation algorithm. At same time,step parameter is mended in order to improve both convergent speed and steadystate performances of the algorithm.1 Blind separation of instantaneous mixed speech signalsBlind separation algorithm of instantaneous mixed speech signals is based onICA technique. Its performances rely on the independence criterion andoptimization algorithms. It also relates to the estimation of the probability densityfunction of speech signal with independence criterion. Normally the exactprobability density function of speech signal is unknown beforehand and usuallythere is no need to do an exact estimation of this function for the source signalseparation. However convergent speed of the algorithm will be improved if anappropriate nonlinear function as an estimation of the function for speech signal isavailable. The feature of speech is often modeled as Laplace distribution function,t-distribution function or hyperbolic secant (sech) square distribution function.Therefore, a modified hyperbolic secant square distribution is proposed as astatistical model for speech signals in this paper. The core function deduced by thismodified function works better than other mentioned two typical distributionfunctions used in speech separation. It can improve convergent speed of theseparation algorithm.The performances of the separation algorithm also depend on the optimizationalgorithms. However, the choice of the step parameter affects the convergent speedand stability of the optimization algorithms. That is the better stability and slowerconvergent speed will appear at the same time if the step parameter is smaller. Onthe contrary, the worse stability and faster convergent speed will appearsimultaneously if the step is bigger. It is a key problem to solve the conflictbetween convergent speed and stability of the algorithm. The EASI algorithm hasbetter performances when compared with the other optimization algorithms bycomputer simulations. A new time varied step parameter is presented for EASIalgorithm in this paper. This step parameter can guarantee faster convergence andbetter stability for the separation algorithms than other existing time varied stepparameters.2 Blind separation of convolutive mixed speech signalsIn real speech environment, the received sensor signals are often convolutivemixtures of the source signals. Each sensor signal has its own phase different fromthat of the others. It can be regarded as the mixtures of source signals convolutedby high order filters.As speech signal separation is conducted in time domain or frequencydomain. There are two primary separation models in the time domain, feed-forwardmodel and feed-backward model. A simulation analysis for feed-forward separationmodel is made in this paper. For the sake of limitation of the algorithm itself, itneeds very complicated calculation to separate signals in time domain. In view ofFourier Transform (FT), which can transform time domain convolutive mixturesinto instantaneous mixtures in frequency-domain, a study of the separationalgorithm in the frequency domain is made.To do frequency domain analysis, Short Time Discrete Fourier Transform(SDFT) is used to transform time domain speech signals to frequency domainbecause of non-stationary of the signals. But the scale and permutation ambiguityof the ICA bring difficulties to the frequency domain separation algorithms. Thesetwo indeterminacies are acceptable in the instantaneous mixed signal separation oftime-domain. The scale and permutation ambiguity are non-fixed at differentfrequency bins, which makes the separated signals still mixed when they aretransformed back from frequency domain to time domain if this indeterminacyproblem has not well solved. The methods to solve this important problem arestudied and simulated by computer simulation in this paper.A lot of calculations are required because of separation at every frequencybins and adjustment of the scale and permutation, though the complexity of thecalculation is reduced in the frequency domain. To this problem, two simple andtentative frequency methods are introduced. These methods can use one or twofrequency bins to accomplish the separation respectively. Though the methodwhich uses one frequency bin is infeasible showed by the simulation, these twomethods give us elicitation for our study.