Fast Fixed-point Algorithm for New Kurtosis by Introducing the Reference Signals

In the blind source separation (BSS) and independent component analysis (ICA),kurtosis is a common contrast measure for non-gaussianity of stochastic signals. The source signals can be extracted or recovered by using different optimization algorithms to find the non-gaussianity maximization points. For instance, the fast fixed-point algorithm based on kurtosis is a very classical one, which has very fast convergence speed. Recently,a family of so-called reference-based contrast criteria have been proposed by Marc Castella etc, and corresponding gradient maximization algorithms have also been proposed, which show very good performance. Inspired by them, the reference-based scheme is applied in kurtosis to construct a new kurtosis contrast function in a similar manner, based on which a novel fast fixed-point algorithm is proposed in this paper. Compared with the classical kurtosis-based fast fixed-point algorithm, this new algorithm is much more efficient in terms of computational speed, which is significantly apparent with large number of samples. The local consistency of this new contrast function is analyzed and proved, and the derivation of this new algorithm is also presented in detail. The performance of this new algorithm is validated through simulations, together with corresponding comparison and analysis.