Algorithms and Applications Research on Independent Component Analysis Based on Negentropy
|School||Harbin Institute of Technology|
|Keywords||independent component analysis negentropy quasi-Newton method image denoising|
Independent component analysis (ICA) is a new signal processing technique for extracting independent sources given only observed data that are mixtures of the unknown sources. It becomes more and more important in wide fields, such as speech signal processing, radar signal processing, telecommunications, pattern recognition, face recognition, image feature extraction, neural computation, medical signal processing and so on. The research of theory on ICA has rapid developments and lots of algorithms were proposed during the past ten years in a large number of journals and conference proceedings. ICA becomes one of the most exciting new topics both in the fields of signal processing and artificial neural now. This dissertation is devoted to the study of several algorithms and their applications for independent component analysis. The paper is organized as follows:Firstly, we introduce in detail the status of independent component analysis in the aspects of algorithms and applications at home and abroad. In addition, we introduce the main research of my paper.Then, some relate mathematical preliminaries, probability, statistics, matrix and information theory, are introduced firstly. We subsequently describe the theory of ICA particularly. We introduce the definition, mathematical model and data pretreatment of ICA. The uncertainty, basic suppositions and traits of ICA are analyzed. Finally, we give two typical indicators of performance for the evaluation of ICA algorithms.Next, the main issues of the research in ICA are discussed. Several classical cost functions of ICA algorithms and their derivations are introduced. The cost functions in the information-theoretic framework are unified.Finally, we introduce the basic idea of quasi-Newton method at first. And then for the cost function of the negentropy maximization, we use single rank Broyden quasi-Newton method and single rank inverse Broyden quasi-Newton method to solve it separately. Two ICA algorithms are given. Making use of these two algorithms, we carry out experiments for super-Gaussian signals, sub-Gaussian signals, as well as their mixed-signals respectively. There is a very good separation. Compared with natural gradient algorithm with the fixed step, the results show that the two algorithms have the higher separation accuracy. Finally, this paper discusses the application of ICA algorithms in image denoising. A kind of adaptive image noise canceling method based on ICA is proposed. We also compare the ICA method with some traditional methods: Median filter and Wiener filter algorithm. The proposed method has the higher SNR and it is suitable to recover the original image when it is polluted by the same noise seriously. Computer simulations illustrate that the method can well eliminate pattern noise.