Underdetermined Blind Source Separation Based On Hybrid Clustering And Compressed Sensing

Blind Source Separation(BSS) became to be a research focus, which emerged over the past ten years, and has its potential applications in many key fields, so BSS has been one of the hottest topics in signal processing. BSS is to recover or estimate the original signals, by using the only known observed mixed signals from the transmission system, without any prior knowledge, or know little about the sources and channels. The famous algorithm of blind source separation is Independent Component Analysis(ICA). However, ICA is a supercomplete/compl-ete problem where the number of observed signals is no less than sources. When the number of observed signals is less than sources, the blind source separation problem is called underdetermined blind source separation. The underdetermined case is more comfort to actual situation, we can determined the number of sensors, so the underdetermined case is more common in the real world.In this paper, underdetermined blind source separation technology of instantaneous mixtures is researched. This problem refers to the mixing matrix identification and source separation. This paper including two parts as follows:(1) The mixing matrix estimation algorithm based on hybrid particle swarm optimization and K-means clustering. The mixing matrix estimation algorithm plays a key role in underdetermined blind source separation. With regards of the fault of traditional K-means clustering algorithm, such as:the initial valve setting is high demand, its easy to fall into local optimal solution and more sensitive to outliers and noise. A novel K-means cluster method based on the Particle Swarm Optimization(PSO) algorithm is presented. In this approach, the stochastic mutation operation is introduced into the PSO, which reinforces the exploitation of global optimum of the hybrid cluster algorithm. In order to reinforce the exploitation of local optimum and improve the estimation accuracy, traditional K-means algorithm is used to explore the local search space more efficiently dynamically according to the variation of the particle swarm’s fitness variance and amend the cluster center by using the method of mesh density. The experimental results show that the new algorithm has the advantages of high stability and estimation accuracy.(2) Source separation algorithm based on compressed sensing. By analysis the similarities of basic mathematical model between the CS and BSS when the mixing matrix is known, we establish the underdetermined blind source separation model based on compressed sensing, and then use the signal reconstruction algorithm of compressed sensing theory to separate the sources, with regards to the high computational complexity and slowly convergence speed of ι1-norm minimization algorithm based on basis pursuit, we use the orthogonal matching pursuit algorithm of compressed sensing to separate the sources, and improved the atom matching method based on inner product of standard orthogonal matching pursuit by using the correlation coefficient. The modified algorithm reduced the computational complexity and shorten the running time of the reconstruction algorithm that doesn’t affect the quality of speech reconstruction. The experimental results show the effectiveness of the algorithm.