Research On Mixing Matrix Estimation For Underdetermined Blind Source Separation

As a powerful signal processing technique,blind source separation(BSS)is an important research field,which has been widely attentioned in digital communications,image processing,and biomedical science and so on.In some actual application scenario,due to the constraint of costs and communication environment,there are only fewer receiving sensors are placed,and the number of sensors are less than the number of sources.In this case,the model of underdetermined blind source separation(UBSS)usually holds more weight than the model of overdetermined blind source separation(OBSS).Compare with the traditional OBSS model,it is more challengeable to solve the UBSS problem.The sparse component analysis(SCA)method is usually adopted in UBSS,and in the SCA,the twostep approach(TSA)is generally used to solve the underdetermined model,which estimates the mixing matrix before recovering the source signals.Therefore,the precise estimation of mixing matrix is very significant in source recovery.According to the difference of mixing model in UBSS,this thesis respectively studies the mixing matrix estimation algorithms under the circumstance of linear instantaneous mixing model and linear time-delay mixing model.Specific research contents and results are listed as follows:(1)For linear instantaneous mixing model,when the sources are sufficient sparse,two algorithms are respectively proposed according to the linear clustering characteristics.Based on the similarity measurement of the observed signals,there are mainly three steps in the first algorithm,including the preprocessing of observed samples,mixing matrix estimation and cluster center calibration.The steps of preprocessing and cluster center calibration makes the algorithm more robusted.The second proposed algorithm based on the ideal of bull 's-eye retrieval,which searchs out the sample with the largest neighborhood capacity in each cluster,and the samples in the neighborhood are selected out to calculate the clustering center as one of the column vectors in the mixing matrix.The simulation results shows the superiority of proposed algorithms on matrix estimation precision and university compared with some existing algorithms.(2)For linear instantaneous mixing model,when the sources are not sufficient sparse,some effective existing algorithms are introduced from different perspective firstly.According to the theorem of independence component analysis(ICA)and Geschgorin disk estimator(GDE),an algorithm based ICA and GDE is proposed,which segments the observed signals with an appropriate interval at first,and then respectively estimates the number of sources in each fragment of data by Geschgorin disk estimator.Finally,on the basis of ICA and the ideal of bull 's-eye retrieval,the mixing matrix estimation is accomplished.The simulation results shows the efficiency of proposed algorithm.(3)For linear time-delay mixing model,according to the sparseness of source signals in time-frequency domain,an algorithm based on delay clustering is proposed,which estimates and clusters the time delay parameters of different source signal to fulfill the mixing matrix estimation.The simulation results turn out that the proposed algorithm has advantage on estimation accuracy of the number of sources and the precision of matrix estimation.