Higher Order Statistics and Their Roles in Blind Source Separation (BSS)
Sattar B. Sadkhan, Nidaa AbdulMohsin Abbas · 2009
Blind Signal separation and independent component analysis are emerging techniques of Data analysis that aim to recover unobserved signals or sources from observed mixture. Such problem requires us to venture familiar second order statistics, because a penalty term involving only pair wise decorrelation would not lead to separation. Source separation can be obtained by optimizing a contrast function, i.e., a scalar measure of sum distributional property of the output. The constant modules property is very specific, more general contrast function are based on other measure, such as entropy, mutual independence, higher order decorrelation, divergence between distribution of output and some model, etc. The contrast function is used here can derived from maximum likelihood principle. The basic BSS model can be treated in several directions, considering for instance, more sensors than sources, noisy observation, and complex signal and mixture, or obtains the standard narrow band array processing / beaminforming model. Another extension is to consider convolution mixture: this result in multi channel blind deconvolution problem. These extensions are of practical importance. Sometimes the researches are restricted to simplest model ( i.e., real signal as many sensors as sources, nonconvolutive mixture, noise free observation ) because its capture the essence of the BSS problem. Normally the BSS approach answers the following questions:- - When is source separation possible? - To what extent can the source signal be recovered? - What are the properties of the source signal allowing for partial or complete blind recovery ?.