Blind Source Separation For Noisy Model

Blind source separation(BSS) is a new information processing technology,itincludes a lot of math knowledge which refers to estimation theory,optimizationtheory,matrix theory,information theory and stochastic signal theory. With thedeveloping of this research field,it has more potential applications incommunication, biomedicine, image processing, speech recognition, submarinesound signal processing and so on.BSS refers to estimate source signals from sensor observations,whilewithout any prior information about transmission channels and the sources .Theblind signal separation could be divided into single channel separateion andmultichannel separation when care about the numbers of mixing channels. BSSproblem could be divided into linear instantaneous mixing model andconvolution mixing model as well as linear mixing and non-linear mixingmodel,which relate to mixing modes of sources. The research of BSS mostlyfasten in multichannel instantaneous mixing model. This paper also researchfor that model. Some information about delay and convolution mixing modeland non-linear mixing model is gave out as additional knowledge.First of all, Theses introduces the basic knowledge of BSS clearly,emphaseson BSS basic model-instantaneous mixing model. Two ambigurites, commonhypotheses conditions and performance evaluating are discussed base on thatmodel. Theses classifies algorithms for instantaneous mixing model into severalparts,mainly about algorithms maximizing non-gaussian,algorithms base oninformation theory criteria and second order statistical information and so on. Thispaper explains principles and realized methods about several typical algorithmsincluding negentropy algorithm,mininum mutual information algorithm,second-order separation algorithm and so on, analyses merits and defects aboutthem. The common point of these different algorithms is finding a lineartransformation and appling it to sensor observations, so as to make output signalsindependent from each other as far as possible.But actual algorithms are mostly developed for noise-free model,sometimes neglect impact of noises,while this impact always exist.This paperresearchs blind source separation for noise model when traditional algorithmsfail to work. This paper present a new preprocessing method for second-orderblind source separation,improve performance when white noise exists becauseof its specific correlated property in time domain.The principle andmathematical derivation course are discussed in detail,the simulated experimentsvalidate the method.In second-order BSS,statistics are calculated base on samples.It is effectiveasymptotically for ergodic stationary sources,but it isn't guaranted when fornonstationary sources,so second-order BSS algorithm degrades. Theses presentsa method which improves the performance of blind separation for second-ordernonstationary sources,through processing parts or whole signals, it make use ofnonstationary and stationary during a short interval. When joint it and the newpreprocessing method , the performance of blind separation for second-ordernonstationary sources in white noise environment is improved.Joint diagonalization can improve second-order BSS.This paper presents aleast square joint diagnalization method,and gives a common matrix form init.General objects of joint diagonalization are correlation matrices.High ordercumulant is introduced in this paper,and a series of cumulant matrices, thesecumulant matrices are also objects of joint diagonalization. Because the sign ofcumulant don't effect the whole separation process,so the method can separateobservations which contain super-gaussian signals,sub-gaussian signals andgaussian signals.Because the linear mixture of gaussian signals is also a gaussiansignal,and the fourth order cumulants of them are the same,so the method can'twork when sources have multi-signals which are gaussian signals,just likenegentropy and minimum mutual information algorithms.But because highorder cumulant of gaussian source is zero,so such algorithm restrain effect ofgaussian noise in joint diagonalization. In the end,theses discusses problems stillto be solved in BSS and further research direction.