Blind Signal Separation Algorithm Based On Independent Component Analysis

In this paper, we propose a approach to blind source separation of linear mixtures of the signals that the observations are contaminated with Gaussian noise.Firstly, we introduce the basic theory of independent component analysis, high order cumulant and the information theory, analyses the principle and characteristic of some classical algorithms.The second, based on the information theory, factor analysis and cross-validation technique were used to estimate the number of sources in and to reduce the power of additive noise, the dimensionality and the correlation among sources. The Kullback-Leibler divergence is chose for ICA contrast function that measures the mutual stochastic independence of the output signals. Applying the natural gradient to minimize the K-L divergence, the learning rule is developed. By combining the t-distribution model with a family of light-tailed distributions (sub-Gaussian) model, we can separate the mixture of sub-Gaussian and super-Gaussian source components. Through the analysis of speech sources and artificially synthesized data, we illustrate the efficacy of this robust approach.The third, since higher order cumulants are insensitive to Gaussian noise, a cumulant-based contrast function is used and the algorithm is developed correspondingly. The utilization of higher order cumulants ensures us that the convergence properties remain unchanged when there is Gaussian noise.