Study On Blind Separation Of Undertermined Mixtures For Low Sparseness

The sparsity of signals has been successfully applied to underdetermined blind signal separation and many algorithms have been developed for this proble m. However, the performance of such algorithms is substantially limited because they are available, only when the sources are extremely sparse(or highly sparse), and sources in real world are not sufficiently sparse as expected. Chances are that the degree of sparsity is so low that even classical algorithms may yield serious deviation(in the estimated sources) or erroneous results. In this thesis, we study low-sparsity based underdetermined BSS. O ur goal is to improve the classical algorithms by relaxing the sparsity of sources and develop more efficient algorithms which work when the sources are just low-sparse. The contributions of this thesis can be outlined in three aspects as follows:First of all, we notice that the SNRs in the shortest-path method, i.e., the l1 norm and the l0 norm, decrease sharply as the signals become low sparse. To overcome these disadvantages, we leverage the sparsity and independency to develop a new statistical sparse decomposition principle(SSDP), where the above problems are avoided and better results can be obtained.Second, we point out that the bottleneck of the first step in the well-known two-step method is the estimation of the mixing matrix, especially in the presence of multiple sources or serious background noise interference. To address this issue, we propose for low-sparsity signals a new underdetermined blind extraction algorithm. By the use of a single source interval method, this new algorithm can estimate a basis vector and extract one source at a time without affecting other basis vectors. In this way, the irrecoverable matrix problem can be avoided, and the source extraction is completed. We also analyze the underdetermined BSE to arrive at certain necessary conditions for unbiased source extraction.Third, we find that in the case of low-sparsity underdetermined BSS, the SNRs of the DUET decay quickly because a strict condition required by the well-known DUET algorithm cannot be fulfilled. In its original setup, DUET requires the sources be disjoint to each other in both time and frequency domains. In this thesis, this condition is relaxed by the use of rotation transform, which replaces the mixing matrix and its mixtures by linear nonsingular matrices. We use rotation transformation twice to propose Imp-DUET and BE-TFMask algorithm in the process of equal and unequal mixing. The two algorithms run the DUET to obtain the source after transforming the mixing matrix and the mixtures. Both theoretical analysis and experimental results suggest that Imp-DUET, as well as BE-TFMask, are much better than the DUET in low-sparsity cases.In addition the contribution above, we further extend the proposed algorithms to cover the case of the speech enhancement where speech and Gaussian noise are mixing with each other. We propose two new algorithms, namely, TFS-DCSE and TFS-SCSE. These two, comparing with the existing spectrum subtraction algorithm, do not require the time interval of pure noise for removing the noise spectrum. Instead, the noisy speech is sampled into two sub-signals by odd-even sampling in the single-channel speech enhancement model, and then, the low sparsity of Gaussian noise and a threshold is used to divide the time-frequency domain of noisy speech into joint and disjoint areas. After that, sparsity of signals can be established in the disjoint areas, and the noise samples scatter on the “right angle type” or “cross” in their scatter plot. Expurgating the noise samples, the single- or dual-channel speech enhancement is completed. In this way, the results can be shown to be much better than the existing algorithm.To sum up, this thesis proposes several improvements to classical underdetermined BSS methods, solving many important problems of underdetermined blind separation in the low-sparsity-signal scenarios. A new idea on speech enhancement is established, by which the bottleneck of interfering Gaussian noise in speech signal processing can be finally removing.