Sequential Blind Source Separation Based Exclusively on Second-Order Statistics Developed for a Class of Periodic Signals

Maria G. Jafari, Wenwu Wang, Jonathon A. Chambers, Tetsuya Hoya, Andrzej Cichocki

Abstract:

A sequential algorithm for the blind separation of a
class of periodic source signals is introduced in this paper. The algorithm is based only on second-order statistical information and
exploits the assumption that the source signals have distinct periods. Separation is performed by sequentially converging to a solution which in effect diagonalizes the output covariance matrix
constructed at a lag corresponding to the fundamental period of
the source we select, the one with the smallest period. Simulation
results for synthetic signals and real electrocardiogram recordings
show that the proposed algorithm has the ability to restore statistical independence, and its performance is comparable to that
of the equivariant adaptive source separation (EASI) algorithm, a
benchmark high-order statistics-based sequential algorithm with
similar computational complexity. The proposed algorithm is also
shown to mitigate the limitation that the EASI algorithm can separate at most one Gaussian distributed source. Furthermore, the
steady-state performance of the proposed algorithm is compared
with that of EASI and the block-based second-order blind identification (SOBI) method.