Research On Underdetermined Convolutive Blind Source Separation Algorithm And Application In Audio Signal Processing

Blind source separation(BSS)is a research hotspot in signal processing.It is widely used in wireless network communication,audio signal processing,biological signal processing,EEG signal processing and image processing.Therefore,it attracts more and more researchers.In the past two decades,the field of blind separation has been developed rapidly and made a series of major breakthroughs.However,there are still several key problems to be solved:(1)source signal separation in the under-determined linear mixture model;(2)mixing matrix estimation and source signal separation in the under-determined convolution mixture model;(3)permutation ambiguity question in time-frequency domain algorithm;(4)source signal number estimation.For these problems,we mainly solve several crucial problems in the BSS from the following aspectsFirst,to the underdetermined linear mixture model,we propose an effective algorithm that combines tensor decomposition and nonnegative matrix factorization(NMF).In the proposed algorithm,we first employ tensor decomposition to estimate the mixing matrix,and NMF source model is used to estimate the source spectrogram factors.Then a series of iterations are derived to update the model parameters.At the same time,the spatial images of source signals are estimated with Wiener filters constructed from the learned parameters.Therefore,time-domain sources can be obtained through inverse short-time Fourier transformSecond,to the underdetermined convolution mixture model,we exploit the algebraic structure of tensor factorization model and expectation-maximization(EM)to provide a new time-frequency algorithm.This is because tensor factorization has an advantage to estimate the channel for the underdetermined convolutive mixture case,and EM algorithm is conducive to faster converge to the desired solution and better source separating property.In the proposed algorithm,we first estimate the mixing matrix by using tensor decomposition,while permutation alignment algorithm is used to deal with the permutation problems.Then,the model parameters are updated using EM algorithm for improving source separation performance.At the same time,the spatial images of source signals are obtained using Wiener filters constructed from the estimated parameters.Furthermore,the time-domain source signals can be obtained through inverse short-time Fourier transformThird,in the conventional separation algorithms,source signal estimation is perforrmed in the frequency-domain,leading to permutation problems and poor separation results Additionally,in the existing EM algorithms,one of the crucial problems is that updating the model parameters at each iterative step is time consumption.We present an improved EM algorithm that combines NMF and time differences of arrival(TDOA)estimation,avoiding the time consumption by properly selecting initial values of the EM algorithm.In the proposed algorithm,NMF source model is used to avoid the permutation ambiguity problem,and acoustic localization can be achieved by transforming the TDOA.Then,model parameters are updated to obtain better separation results.Meanwhile,the source signals are separated using Wiener filtersAt last,source number estimation is an essential task in underdetermined convolutive blind source separation,and effective channel order determination is also a challenging issue.For solving the two problems,the classical methods are based on information theoretic criteria However,these are prone to the underestimation and overestimation of the number of sources in the underdetermined case.To compensate for this shortcoming,in this paper we propose two algorithms based on higher-order tensors.First,an improved algorithm is presented to estimate the number of sources.By transforming the tensor into a matrix,the eigenvalues of the resultant matrices are used to estimate the number of sources.Additionally,we employ higher-order tensors to detect the effective channel order,and confirm the relationship between the number of sources and the effective channel order in the convolutive mixture modelTo sum up,this paper mainly studies the problem of blind source separation in the underdetermined linear mixture and underdetermined convolution mixture case.To the permutation ambiguity in time-frequency domain algorithm,an improved time-frequency domain algorithm is proposed.Meanwhile,source number estimation is studied,and the mathematical relationship between the number of source signals and the effective channel order is determined.At the end of the paper,the innovations and research achievements of this paper are elaborated.At the same time,the future work is prospected.