Underdetermined Blind Source Separation Mixing Matrix Estimation And Source Signal Recovery Method

Blind source separation has received much attention from researchers in the field of signal processing since it was proposed.It has become the first choice of signal processing when the source signals and transmission channel are unknown.It has been widely used in many different fields such as speech recognition,medical signal analysis,wireless communication and fault detection.In reality,the underdetermined blind source separation is more common and has more applications,so it is valueable to do deep research on it.Sparse component analysis(SCA)is the main method to solve the problem of underdetermined blind source separation,which usually consists of two steps: estimate the mixing matrix first and then reconstruct the sources.Such algoriths rely on the sparseness of the signal.In this thesis,based on the current domestic and foreign research algorithms,aiming at the poor sparsity of source signals,the mixing matrix estimation and source signal recovery algorithms for underdetermined blind source separation are studied.The main contents of this thesis are as follows:Firstly,introduce the system model and basic knowledge of underdetermined blind source separation and sparse component analysis theory.Several current mainstream mixing matrix estimation algorithms and source signal recovery algorithms are described.Then,the evaluation criteria for the performance of these two kinds of algorithms are given.Secondly,for the source signals with poor sparsity,a single source detection algorithm is firstly introduced to improve the signal sparsity.The detection identifies the single source points by comparing the normalized real and imaginary parts of the TF coefficient vectors of the mixed signals.Then,we study a robust similarity-based clustering method(MSCM).The MSCM algorithm has higher estimation accuracy when the number of source signals is unknown.But it is affected greatly by noise and the calculation is complicated.In view of this feature,a mixing matrix estimation algorithm based on piecewise objective functions is proposed.By processing low energy points,the proposed algorithm has great robustness against noise.And the piecewise objective functions can select more suitable objective functions for clustering under different signal-to-noise ratios,which avoids the complicated parameter design while improving the estimation performance.Finally,a classic algorithm of signal recovery using the space theory and a modified subspace algorithm are introduced.The modifide algorithm replaces the assumed number in the classical algorithm by pre-estimating the real number of source signals at any time-frequency point,which improves the performance of the algorithm.But at the same time,the computation of the algorithm increase greatly.Under this circumstance,a simplified algorithm for the modified subspace algorithm is proposed.In the proposed algorithm,the zero TF points is pre-zeroed,so the number of time-frequency points involved in recovery traversal is reduced,which can effectively reduce the computational complexity.