Algorithms Of Blind Sources Separation In Time-Frequency Domains

Blind source separation (BSS) is to recover the sources form the observations only,without the information about the source signals or the mixing process. As a powerfuldata representation and signal processing tool, BSS has become a very important topicof research and development in many areas, especially wireless communications,speech signal processing, array signal processing, image processing, biological signalprocessing, signal recognition, exploration seismology, econometrics, etc.Focusing on this theme, some BSS approaches for non-stationary signals arediscussed in this dissertation.For non-stationary signals, such as speech signals, music signals and EEG, jointtime-frequency analysis(JTFA) can study these signals in both the time and frequencydomains simultaneously, using various t-f representations. This method, hence caneffectively extract the local time-varying characteristics of non-stationary signals andhas better “microscopic” advantage compared to the time domain or frequency domainrepresentation.Based on the bilinear JTFA or linear JTFA, some BSS approaches exploiting thediversities in the t-f signatures of the sources can be obtained.Firstly, the location features of auto-and cross-terms from the multi-componentssignals and their relationship between the Wigner-Ville distribution plane and ambiguityfunction plane are discussed in this dissertation. Then, a high performance kernel isstudied and its t-f distribution、its desirable properties and its calculation algorithm arederived. And, its parameter choice based on Boashash’ performance indicator isproposed. Moreover, a high-resolution t-f BSS approach is developed based on the t-fjoint diagonalization method, proposed by Belouchrani, A and Amin, M.G. Thisapproach includes first whitening mixed signals, then constructing a set of t-f matricesusing the proposed t-f distribution, finally a Jacobi joint diagonalization of a combinedset of t-f matrices to estimate the mixing matrix and the source signals. In addition, aBSS algorithm based on rearrangement t-f spectrum is proposed. This algorithmexploits the rearrangement spectrum mechanism and adopts smooth pseudo Wigner-Ville distribution to eliminate cross-terms interference. By use of the techniquesproposed in this dissertation, the improved performance of BSS of music signal, speechsignals has been achieved. Secondly, a linear t-f BSS approach adopting Stockwell transform or generalizedStockwell transform to obtain multi-resolution characteristics are proposed. Thisapproach uses Stockwell transform or generalized Stockwell transform to derive t-fdistribution of mixed signals and then constructs different t-f ratio matrices, proposedby M.Puigt and Y.Deville. Then, it detects single source occurs to identify each elementof the mixing matrix and hence obtains the estimated signals. This approach can avoidthe cross-terms interference from bilinear t-f distributions and has the multi-resolutioncharacteristics. Therefore it may be more suitable to separate mixed-signals containingmany high-frequency components and low-frequency components simultaneously.Thirdly, in real life, there is a variety of noise present in the observations. How toobtain better noise suppression and robustness is a real problem as the structure ofsignals are corrupted by noise. In this dissertation, source noise is discussed and a BSSapproach based on Hough transform is proposed. This approach is developed whichincludes firstly calculating the t-f distributions of observed signals by Wigner-Villedistribution, and using the Hough transform to convert the signals detection to find thelocal peak values in the parameter domain though considering this t-f distribution as animage, finally a joint-diagonalization of a combined set of t-f distributions chosen byauto-term theory to estimate the unitary matrix, the mixing matrix and the sourcesignals. The effect of spreading the noise power while localizing the source energy inthe parameter plane amounts to increasing the robustness of the proposed approach withrespect to noise.