Blind Signal Separation Algorithm Research Based On Statistic Theory

When signals are processed, its prior knowledge is usually unknown. And it is also difficult to observe the transmission channel information between signals and sensors. This kind of signals could be called "blind source". In a complex environment with many sources, the sensors receive not only useful information, but also additive noise. Technology of recovering blind source signals from observed mixture signals is called blind signal separation (BSS). BSS technology has been wildly used in speech recognition, image processing, biomedicine signal processing, telecommunication, system monitoring, measure economics et al. In this paper, based on the knowledge of mathematics statistic and optimization, we mainly study the theory and algorithm of linear mixed problem in blind signal separation. The efficacy of our algorithm is demonstrated by computer simulations.In our paper, we introduce the study background and the broad application foreground of blind signal separation in our lives firstly. After giving the simple mathematic model and description, we generalize the development history, the current main research institutions and scholars, and the shortcomings of blind signal separation research.Secondly, we study a BSS algorithm based on quasi-Newton method in time region. Using joint diagonalization of correlation matrices as the cost function, we propose a new algorithm which separates source signal based on quasi-Newton's DFP method. The new algorithm improves the convergence rate. Validity and performance of the new algorithm are demonstrated by four speech signals computer simulations.Thirdly, we study a modified fast ICA algorithm based on four-order cumulant. The basal theory and method of independent component analysis (ICA) are introduced. Using the four-order cumulant as criterion, we analysis the traditional fast ICA algorithm; and then propose a new modified fast ICA algorithm which replaces the iteration steps of fast ICA algorithm by improved Newton iteration method. Compared with two kinds of algorithm's results on wave signals and speech signals simulations, dates show validity of the modified algorithm.