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

An algebraic principle for blind source separation is presented in this pap er. This separation principle identifies a (smaller) set of equations whose solutions can blindly extract non-Gaussian signals. The concept of "M th-o rder uncorrelatedness" is introduced and it is proven that for Mth-order un correlated source signals, signals with nonzero kth-order cumulant (2 < k l ess than or equal to M) can always be extracted by setting a small set of k th-order cross-cumulants of output signals to zero. The set of kth-order cr oss-cumulants specified here is a sub-set of those used by other existing m ethods. The relationship between the algebraic principle and several existi ng algorithms is presented. The contributions of this principle are the red uction of the number of cross-cumulants used and the flexibility it affords in designing algorithms for blind source separation. (C) 1999 Published by Elsevier Science B.V. All rights reserved.