Research On Algorithms For Blind Source Separation In Nonstationary Environments

Blind source separation (BSS) aims to extract independent but unobservered source signals from their mixtures captured by a number of sensors without knowing the mixing coefficients. Over the past two decades, the problem of BSS has received much attention in various fields, such as speech and audio processing, image enhancement and biomedical signal processing. The main works can be summarized as follows:1. An adaptive improved natural gradient algorithm for blind separation of instantaneous mixtures of independent sources is proposed. First, inspired by the well-known back-propagation algorithm, we incorporate a momentum term into the natural gradient learning process to accelerate the convergence rate and improve the stability. Then, an estimation function for the adaptation of the separation model is obtained to adaptively control a step-size parameter and a momentum factor. The proposed natural gradient algorithm with variable step-size parameter and variable momentum factor is therefore well suited to blind source separation in a time-varying environment. The expected improvement in the convergence speed, stability and tracking ability of the proposed algorithm is demonstrated by extensive simulation results in both time-invariant and time-varying environments. The ability of the proposed algorithm to separate extremely weak (or badly scaled) sources and many sources is also verified. In addition, a block recursive approach for blind source separation is presented. Firstly, based on natural gradient and nonlinear principal component analysis, a matrix equation is obtained by block recursive updating,and then the matrix equation is solved using QR factorization and back substitution to obtain the optimal separating matrix. Compared with other existing recursive-type BSS methods, the proposed algorithm is feasible to real-time processing, and the choice of the forgetting factor is simple. Compared with other block processing methods, the proposed algorithm has fast initial convergence speed.2. An efficient variable forgetting factor recursive generalized eigen-decomposition algorithm is developed for blind separation of non-white sources when the mixing matrix changes abruptly. We derive a new recursive update equation for the multiplication of a cross-correlation matrix and the inverse of a covariance matrix with compact form and low computational complexity. The generalized eigenvectors are recursively estimated by using the approximated power method and the deflation procedure. Without additional priori information of the mixtures, we propose a novel on-line decision rule to track the abrupt variations of the mixing matrix and then a variable forgetting factor recursive generalized eigen- decomposition algorithm for BSS is presented for the time-varying environments. The improved tracking ability and steady-state accuracy of the proposed algorithm are validated by the computer simulation results.3. By exploiting of speech nonstationarity, a method for estimating the number of sources from instantaneous mixtures of speech signals with unknown source number is presented, and then the sources are extracted. The first dominant generalized eigenvector is estimated by recursive generalized eigen-decomposition. The mean similarity curve of the estimated generalized eigenvector is introduced to fit inter-channel interference curve, and then"High Similarity Intervals"are extracted to approach"Separation Interval". Moreover,"High Separation Intervals" are obtained by extracting"High Similarity Intervals"with better separation performance and eliminate"Mixtures Interval". Final, the number of the sources is estimated with multistage clutstering techniques and the corresponding sources are extracted. The proposed algorithm can avoid suffering the error propagation of the deflation technique, which exists in all sequential algorithms.4. A new post-processing method for convolutive mixtures blind speech separation is proposed. It utilizes multi-channel signal enhancement to suppress spatial interference and background noise. Due to imprecision for solving the permutation ambiguity problem, frequency domain blind source separation has its fundamental limitation in separation quality. To overcome that, by splitting spectrograms, the M×N multi-input multi-output (MIMO) system will be converted into N single-input multi-output (SIMO) system in frequency domain blind speech separation system. Furthermore, to attenuate spatial interference from competing sources and background noise, the multi-channel signal enhancement method is exploited to reconstruct source signals from the N SIMO system respectively. The separation performance of the proposed algorithm is demonstrated by experiments.