Independent Component Analysis Of The Research And Application Of The Offline Algorithm

The independent component analysis (ICA) is a branch of the Blind source separation, which has become an important part in signal processing and data analysis. Most current algorithms only work well in special conditions, because of the abnormity of signals in the real world. Now, the research in the ICA arises much passion and the ICA has brought about many applications. The primary results the writer has got are as the following:After a whiting process, it is a key to find an orthogonal matrix to throw away the high-order redundant information between components. Orthogonal matrixes have special structures, and every row vector of them can be taken as a plot, which may be parametrized in N-sphere space. Through the research of structures of orthogonal matrixes, the writer finds a parametrized matrix, which can express all the orthogonal matrixes. Through analysing uprightness between related high-order planes and the number of required parameters, we get the maturity of this method. In succession, some analysis is given out for the randomicity of the parametrized matrix. At last, there is a parametrized matrix for probability of 1. And then, the way to resolve the optimization problem is Genetic Algorithms. In substance, through throwing away the restriction of orthogonal condition in the optimization problems, there will be an optimization problem without restriction. The validity of this algorithm is proved in the experiments of different kinds.In addition, the measures to weigh the independence of signals are key-concept in the ICA. In general ways, it uses concepts in the information theory, such as entropy. The writer gives out a way, in which we take the magnitude of the independence between signals as parameters of some special kinds of functions, to measure the independence of signals from function optimization, and the values of these functions reflect the magnitude of the independence. Of course, the means on measuring independence this way needs to be validated in practice.It is a difficult problem in the bioengineering to extract ECG signals. In this paper, through ICA, the writer achieves results again, which proves that the ICA is a...