Reseach On Underdetermined Blind Source Separation In Time-Frequency Domain

Blind source separation (BSS) aims to recover multiple original sources mixed through unknown channels. The traditional BSS technique is based on independent component analysis (ICA). The classic ICA theory can only separate stationary non-gaussian signals and cannot be applied to the underdetermined case in which the number of sources is larger than the number of sensors. Many signals have the non-stationary property in our life, such as, the speech sources. So, finding the new approach methods to solve the non-stationary signals in underdetermined mixtures is necessary. Sparseness-based approaches are of interest because they can handle the non-stationary signals in underdetermined mixtures. There are many signals being not very sparse (soft-sparse) in our environments, such as the time-frequency (TF) domain of speech signals. The soft-sparse signals allow multiple signals coexisting in a single TF point. This thesis is mainly about the soft-sparse signals of the underdetermined blind source separation (UBSS) problem. The main contributions of the thesis are as follows:(1) The mixing matrix estimation of the instantaneous UBSS problem is studied for the method that is based on TF domain. The key problem of the TF domain mixing matrix estimation is the selection of the TF points that are only occupied by a single signal. A TF masking method of the selection of the single signal TF points was proposed in this thesis, the method is based on the Wigner-Ville and short time Fourier transform (STFT) in TF domain. Then the clustering method is being implemented of the single signal TF points to estimate the mixing matrix. Experimental results show that, compared with other conventional algorithms, the TF masking method can separate to a higher performance.(2) The convolutive filters estimation of the convolutive UBSS problem is studied for a direct estimation system. First, short time Fourier transform is done to the mixtures of time domain. Then, a normalized "bottom up" clustering process was proposed to cluster mixing vector of the mixing filtering estimation. Compared with the non-normalized cluster mixing vector estimation method, the proposed method in this thesis can obtain better performances.(3) A new source recovery approach called Inverse Truncated Mixing Matrix (ITMM) method is proposed to the signals being not very sparse. First, the mixing matrix is truncatted into some square matrices. Then, multiplying is applicated with mixtures of time-frequency domain and the inverse square matrices. Finally, the sources can be extracted with some sets by the sparse signals property.ITMM method allows multiple sources coexist in a single time-frequency plane as long as the number of coexisting sources is not larger than the number of observations. Experimental results show that, compared with other conventional source recovery algorithms, the ITMM algorithm can separate speech and audio sources to a higher performance.(4) In order to decrease the probability of missing some data points or being added by noises in the Inverse Truncated Mixing Matrix (ITMM) algorithm. A two-stage frequency domain method is proposed to blind source separation for underdetermined instantaneous mixtures. First, the mixing matrix is estimated and source recovery with ITMM algorithm in frequency domain. Then, in order to retrieve the missing data and remove the noises, matrix completion technique is applying to each estimated source with traditional ITMM algorithm in frequency domain. Simulations showed that, compared with traditional ITMM algorithms, the proposed two-stage algorithm has better performances. Simulation results show that this approach yields good performance.