A Research Of Underdetermined Blind Source Separation Based On Compressed Sensing Of Reconstruction Algorithm

Compressed sensing is a theory between the information science andmathematics rising in this years, this theory brings revolutionary breakthrough forsignal sampling technique. It uses an adaptive linear projection method to keep theoriginal structure of signal basing on the sparsity characteristics of the original signal,and samples the signal at a speed much lower than the Nyquist frequency, finallythrough solving the numerical optimization problem to reconstruct the original signal,It offers a solution to the problem of the storage and transmission of massive data.As one of the most popular branch of the field of signal processing, the blindsource separation theory having a reliable theoretical basis and many aspects ofapplied potential, and obtains many progress in many practical applications. Theproblem of underdetermined blind source separation naturally meets the needs of thetheory model of compressed sensing; therefore, the method of underdetermined blindsource separation based on compressed sensing becomes a new method to slove theproblem of underdetermined blind source separation, and it has a good applicationprospect.This paper proposes a new reconstruction algorithm aiming at the insufficient ofcurrently greedy iterative reconstruction algorithm in compressed sensing theory; Andputs forward a kind of underdetermined blind source separation method based oncompressed sensing. The main work of this paper is as follows:Firstly, the thesis introduces the technology research background, significance,research status, future development trends of blind source separation and compressedsensing, describes their own theoretical framework, analyzes the separation methodsof blind source separation methods and the reconstruction algorithm of compressedsensing, and analyzes their properties by simulation.Secondly, based on the analysis of greedy iterative reconstruction algorithms incompressed sensing, the author draws a conclusion that there are improved space inthe reconstruction accuracy of matching pursuit algorithm as well as the subspacetracking algorithm, So the author proposes a adaptive step-size piecewise matchingpursuit algorithm, the iterative process is divided into two sections in this algorithm:in the early iteration, it uses a big iterative step-size, in order to save thereconstruction time; at the later period of iteration, it uses a small iterative step-size, in order to improve the reconstruction precision. At last checks its performanceimprovement through the simulation results.Finally, based on the truth that the underdetermined blind source separationmeets the condition of compressed sensing compressed model, the author transformsthe underdetermined blind source separation problem into the problem of sparsesignal reconstruction in compressed sensing theory, and uses compressed sensingreconstruction algorithm to separate the mixed signals in two steps: the first, usingK-mean clustering algorithm to estimate the mixing matrix; and then usingcompressed sensing reconstruction algorithm to separate the source signals with thehelp of the estimation of mixing matrix. At last the thesis analyzes the feasibility andproperties of this method through the simulation results.