A Study Of Independent Component Analysis Algorithm

Blind signal separation is a new research field recently rising and it has a widely application in practice. Under the condition without knowing the source and mixing matrix, independent component analysis can solve the problem of blind signal separation soundly with the assumption that the sources are mutual independent. The work of this paper is extended from independent component analysis algorithm. In this thesis the background and the history of blind signal is introduced and the theory as well as concepts of independent component analysis are given. Some independent component analysis algorithms and their traits are discussed and the priors used in independent component analysis are summarized in this thesis.Among the prime process of independent component analysis, whitening is rather important. For the whitening process, its variance is studied. At the same time, for some independent component analysis algorithms it is dispensable to orthogonalize their output matrix. The existing orthogonalization algorithm is generalized based on its analysis and the new algorithm with higher convergence speed is proposed.In this thesis the existing relative gradient is generalized and the new concept of generalized gradient and its application in the independent component analysis algorithms are proposed. For any algorithm its stability must be guaranteed, the deduction of the stability of independent component analysis algorithm in this thesis unified some results on stability.In independent component analysis, how to decide the probability density functions of the sources is very critical. Three methods are discussed: using fixed probability density function, adaptive probability density function and approximating the score function. At last under which linear transform the probability density function is invariable is studied.