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This paper deals with the optimization of kurtosis for complex-valued signals in the independent component analysis (ICA) framework, where source signals are linearly and instantaneously mixed. Inspired by the recently proposed reference-based contrast schemes, a similar contrast function is put forward, based on which a new fast fixed-point (FastICA) algorithm is proposed. The new optimization method is similar in spirit to the former classical kurtosis-based FastICA algorithm but differs in the fact that it is much more efficient than the latter in terms of computational speed, which is significantly striking with large number of samples. The performance of this new algorithm is confirmed through computer simulations.

This paper deals with the efficient optimization problem of Cumulant-based contrast criteria in the Blind Source Separation (BSS) framework, in which sources are retrieved by maximizing the Kurtosis contrast function. Combined with the recently proposed reference-based contrast schemes, a new fast fixed-point (FastICA) algorithm is proposed for the case of linear and instantaneous mixture. Due to its quadratic dependence on the number of searched parameters, the main advantage of this new method consists in the significant decrement of computational speed, which is particularly striking with large number of samples. The method is essentially similar to the classical algorithm based on the Kurtosis contrast function, but differs in the fact that the reference-based idea is utilized. The validity of this new method was demonstrated by simulations.