Research On Mixing Matrix Estimation And Source Signal Recovery For Undetermined Blind Source Separation

Blind source separation?BSS?is an effective method to solve the signal separation.BSS has been successfully applied to biomedical engineering,audio signal processing,image signal processing and communication signal processing,which has important academic value and application prospect.Underdetermined blind source separation?UBSS?aims to recover the source signals only according to the observed signal received by the sensors,when the number of sensors is less than that of the source signals.In this paper,we study the mixing matrix estimation and the source signal recovery algorithm.The concrete contents and achievements are summarized as follows.?1?In the case where the source signal is sufficiently sparse,the current blind estimation methods of mixing matrix based on single-source points detection in time-frequency domain share one common problem that the time resolution and frequency resolution cannot be optimized simultaneously,which affects single source detection efficiency.A new blind estimation method based on modified time-frequency single-source detection is proposed in order to solve the problem.According to the uncertainty principle,Gabor Transform is applied to improve the time-frequency resolution without changing the linearity of the hybrid model,so as to improve the accuracy of single-source detection.The simulation results show that the accuracy of the proposed method is improved when compared with the conventional methods.?2?An algorithm for mixing matrix estimation in underdetermined blind source separation based on homogeneous polynomial representation is proposed,in order to address the issue of blind identification of mixing matrix when the source signal is not sufficiently sparse.Firstly,the observed signal subspaces?hyperplanes?are identified by fitting polynomial,differentiation and spectral clustering.Then,columns of mixing matrix?up to scaling and ordering?are estimated using the intersection lines between clustering planes.Depending on algebraic-geometric method,the accuracy of the estimation of mixing matrix obtained by the algorithm proposed can be effectively improved,and is not affected by convergence.The simulation results indicate that the algorithm proposed has obvious advantages on estimation accuracy.Additionally,the single-source and multi-source points of source signal can be detected simultaneously,which increase the robustness of algorithm.?3?The recovery precision is greatly influenced by the step size and the complexity of the algorithm is high,when the radial basis function?RBF?network based sparse recovery algorithm is applied to source recovery in UBSS.An algorithm for source recovery based on RBF network is proposed in order to solve this problem.On the basis of RBF,the modified Newton algorithm is introduced into the proposed algorithm to minimize the approximate?₀ norm,which can avoid inaccurate recovery caused by unsuited step size.Aiming at reducing complexity further,we propose a novel source recovery algorithm in UBSS,which can result in better accuracy and lower computational cost.Single-layer perceptron is introduced in the algorithm.What's more,the optimal learning factor is calculated and a descent sequence of smoothed parameter is used during iteration,which improves the performance and significantly decreases computational complexity of the proposed algorithm.The simulation results reveal that the algorithm proposed can recover the source signal with high precision,while it requires low computational cost.In this paper,we only focus on the UBSS for the linear instantaneous mixing model and do not apply to the signal separation in the complex environment with multipath effect.The more reasonable model is the convolutional mixing model.Hence,UBSS for convolutional mixing model is a challenge for subsequent research.