Abstract: Independent Component Analysis(ICA)is an effective method to solve the blind source separation (BSS) problem.FastICA,which take central limit theorem as the starting point,uses the optimization algorithm of fixed-point iteration,and converges fast and steadily.Due to the disadvantage of central limit theorem,the FastICA no longer applieds when we extract weak signal.This paper explored the FastICA theoretically and experimentally,and addressed this problem by proposing new ideas.Based on the FastICA,we use independent component analysis (ICA-R) to establish proxintity measure combined with the conception of extrapolation in minimize weighted norm,in the case of a part of power spectrum of the source signal is known.Thus,the targeted weak signal can be extracted by integrating the measurement into FastICA in a constrained way.Experiments show that the proposed algorithm is effective for both analog and real signal.

Key words: Weak signal extraction,FastICA,Central limit theorem,Independent component analysis with reference,Minimize weighted norm