Study On Underdetermined Blind Source Separation Of Relaxed Sparse Mixtures

Underdetermined Blind signal separation is the linear mixing problem that the number of the observed signals is less than one of the sources. It is usually resolved using the two-step method based on sparse representation of the signal. The first step is to estimate the marix and the second step is to estimate the sources. Relaxed sparse condition doesn’t completely satisfy the sparse condition. It is relaxed sparse and underdetermined blind source separation that is studied in this thesis. Its purpose is to improve the SNR of the estimated sources and to obtain the good sources. There are four contributions in this thesis.Firstly, the mixing of the speech and Gaussian noise, which is belonged to speech denoising, is considered based on underdetermined blind source separation. The mixtures are not sparse but they are relaxed sparse when the speech is mixed into the noises. We propose a speech denoising based on sparsity according to the relaxed sparse. By the threshold in speech enhancement, the algorithm splits the time frequency domain of the observed signals into two areas that is in Non-Disjoint areas (NON-DA) and disjoints Area (DA). The algorithm adopts the different denoising strategies. In the NON-DA, it throws away the signals. In the DA, it deletes the noise on the "cross" and uses the smooth filter to compensate the distortion.Secondly, the sparsity is a strick condition and the relaxed sparsity is a relaxed condition which is near to the actual case. Time-frequency mask method is far away the real circumvent as it uses the sparse condition. To obtain a good result, a blind extraction algorithm via time-frequency mask is proposed. The algorithm combines the non-completely sparse blind extraction with the DUET. It can compute the extraction vector of the source and the normal vector of the source direction; it also renews the mixtures and the mixing matrix using a linear transform. Subsequently, the source is recovered using time-frequency mask. Although it has higher computation complexity theoretically, its performance is obviously better than the DUET.Thirdly, based on the blind extraction via time-frequency mask, we continuly study the relation between the rotatotion transform and the DUET algorithm. An improved DUET algorithm is proposed in this thesis. The algorithm rotates the mixtures and mixing matrix using a rotation matrix, which is formed by any two columns in the mixing matrix, and then do DUET algorithm. Because the results are different in DUET algorithms under different rotations, the algorithm sums the estimated signal to improve the distortion.Finally, a matrix estimation of sparse component analysis is proposed for k-SCA condition based on the normal vector of hyperplain. The algithm is the extention of the underdetermined BSS based on the normal vector of hyper plain. It gives a definition of k-component interval and the method to identify it. The algorithm is to detect the samples of k-SAC and estimate the matrix.The above four works are main contributions of this thesis. We also do many experiments to testify our theory and algorithms in this thesis.