An algebraic principle for blind separation of white non-Gaussian sources

An algebraic principle for blind source separation is presented in this paper. This separation principle identi"es a (smaller) set of equations whose solutions can blindly extract non-Gaussian signals. The concept of `Mth-order uncorrelatednessa is introduced and it is proven that for Mth-order uncorrelated source signals, signals with nonzero kth-order cumulant (2(k)M) can always be extracted by setting a small set of kth-order cross-cumulants of output signals to zero. The set of kth-order cross-cumulants speci"ed here is a sub-set of those used by other existing methods. The relationship between the algebraic principle and several existing algorithms is presented. The contributions of this principle are the reduction of the number of cross-cumulants used and the #exibility it a!ords in designing algorithms for blind source separation. ( 1999 Published by Elsevier Science B.V. All rights reserved.