Research Of Some Problems On Independent Component Analysis

Blind Signal Processing (BSP) is one of the most cutting-edge disciplines in signal processing field, and it has many potential applications. While independent component analysis (ICA) is a very important new technology of blind signal processing developed in later 90's of 20th century. Through the successful use of higher-order statistics information, it perfectly solves the traditional problem of blind source separation (BSS). Among all the methods, the fast fixed point algorithm (FastICA) based on approximation of negentropy has become one of the most popular ICA algorithms. For its outstanding performance in blind identification and feature extraction, ICA has rapidly growing applications in various fields, e.g., telecommunication systems, speech processing, image enhancement and biomedical signal processing.ICA's current research focuses on two aspects. One is the theoretical research on basic model of ICA; while another considering some extensive problem of the basic model.In this paper, while generally and systematically summarizing the current ICA algorithms from the mathematical point of view, the above two parts of research were all considered. Contribution of the article mainly includes the following two parts: First is the study on the convergence of basic ICA. When the measurement function on independence is determined, ICA can be attributed to a simple optimization problem. And the core issue needs to be considered of optimization problem is whether local optimal solution of the measurement function exists, which optimization algorithm should be used, and whether the optimization method can avoid to get a local optimal solution? Some scholars of Europe pointed out in their latest research results: Although the minimum of mutual information and the maximum of non-Gaussian property is a very strict measurement function of independence, they do exist the local optimal point in some cases. To solve this problem, this paper presents the application of global optimization methods (such as particle swarm optimization algorithm) to improve the stability of convergence.Second, since the signal in practical application is generally time-series with a certain amount of time structure information. This article attempts a new way to utilize this information to further improve the separation effect of the traditional ICA. This basically belongs to the extensive problem of the basic model of ICA problem. Different from the general way to consider the problem, this article doesn't want to change the measurement function for optimization, while propose to decompose the observing signal in time domain before ICA separation process, to make the input data more satisfied with the basic model of ICA, and then after the separation process of ICA, the output signal is reconstructed, thus indirectly using the time structure information to improve the quality of separation. Several numerical experiment results also verify the effectiveness of the improvement.In the end of this article, conclusions and outlooks are drawn in the dissertation.