Sequential blind extraction of instantaneous mixtures with arbitrary rank
Sanqing Hu, Derong Liu, Jun Wang · 2006
In this paper, we present new extractability conditions for blind source extraction of linear instantaneous mixtures. Two general conditions for source extraction of arbitrarily mixed nonzero sources are presented. A sufficient condition is provided to guarantee that sequential extraction can be continued. We also show an important property for inseparable mixtures; that is, any two extracted signals involving the same sources are proportional to each other. For sub-Gaussian or sup-Gaussian source signals with only mutual independence, cost functions based on fourth-order cumulants are introduced to sequentially extract all separable single sources and all inseparable mixtures. By minimizing the cost functions, gradient-based methods are developed. Our algorithms are guaranteed to converge. Finally, simulation results show the operation characteristics and the effectiveness of our methods