A computationally affordable implementation of an asymptotically optimal BSS algorithm for ar sources

The second-order blind identification (SOBI) algorithm for separation of stationary sources was proved to be useful in many biomedical applications. This paper revisits the weights-adjusted variant of SOBI, known as WASOBI, which is asymptotically optimal (in separating Gaussian parametric processes), yet prohibitively computationally demanding for more than 2-3 sources. A computationally feasible implementation of the algorithm is proposed, which has a complexity not much higher than SOBI. Excluding the estimation of the correlation matrices, the post-processing complexity of SOBI is O(d
⁴
M), where d is the number of the signal components and M is the number of covariance matrices involved. The additional complexity of our proposed implementation of WASOBI is O(d
⁶
+ d
³
M
³
) operations However, for WASOBI, the number M of the matrices can be significantly lower than that of SOBI without compromising performance. WASOBI is shown to significantly outperform SOBI in simulation, and can be applied, eg., in the processing o low density EEG signals.