Blind Source Separation Based On Improved Natural Gradient Algorithm

Blind source separation is a newly developed method for the separation of unknown mixed signals in the field of signal processing.After decades of continuous research and development,blind source separation has become a hot topic in many subject areas,with many potential application values,and has been widely used in many fields.Since the 21 st century,the research direction of blind source separation has been divided into two aspects,one is to solve the convolution mixing problem and the underdetermined problem,and the other is to optimize the separation algorithm and improve the separation performance of the algorithm.Based on the study of blind source separation theory and natural gradient algorithm,An improved natural gradient blind source separation algorithm is proposed for the shortcomings of the algorithm.For the separation of noisy blind sources,the algorithm is further improved by introducing momentum factor,and combined with wavelet denoising principle,a blind source separation algorithm based on wavelet denoising and improved natural gradient is constructed.The natural gradient algorithm is a commonly used and important method in blind source separation,with fast convergence speed and good separation performance.The step size of the standard natural gradient algorithm is fixed,but there is a contradiction between the convergence speed and the steady state error,and the convergence speed of the intersymbol interference is very slow.In response to the above problems,an improved natural gradient algorithm is proposed.First,construct a step-and-step iterative update function to achieve adaptive selection of the step size in the algorithm.Then the Frobenius norm constraint is imposed on the improved algorithm,which accelerates the convergence speed of inter-symbol interference.Finally,the effectiveness of the algorithm is verified by experiments.The experimental results show that the proposed algorithm has faster convergence speed and less steady-state error,and has better separation performance.In a practical application environment,the acquired mixed signal usually contains a noise signal.Studies have shown that many blind source separation algorithms,such as FastICA,EASI and approximate joint diagonalization,in the case of noise,the separation effect of the algorithm will be seriously reduced,and even the source signal can't be effectively separated.For the separation of noise-containing blind sources,in order to improve the separation effect and stability of the algorithm,the mixed signal needs to be denoised.Since the wavelet denoising method has a very good denoising effect,and its mathematical model is relatively simple,the prior information of the source signal is relatively low.Therefore,the wavelet soft threshold is selected to denoise the noisy mixed signal.The natural gradient algorithm is further improved by introducing a momentum factor,and the step factor and the momentum factor are adaptively adjusted by the feedback of the performance index.In the case of noisy signals,a blind source separation method based on wavelet denoising and improved natural gradient is constructed.Through simulation experiments,data from various performance evaluation indicators indicate that,the natural gradient algorithm improved in this paper has better separation performance than other algorithms,and the algorithm has better noise resistance and stability.