A fast algorithm for one-unit ICA-R

Independent component analysis (ICA) aims to recover a set of unknown mutually independent source signals from their observed mixtures without knowledge of the mixing coefficients. In some applications, it is preferable to extract only one desired source signal instead of all source signals, and this can be achieved by a one-unit ICA technique. ICA with reference (ICA-R) is a one-unit ICA algorithm capable of extracting an expected signal by using prior information. However, a drawback of ICA-R is that it is computationally expensive. In this paper, a fast one-unit ICA-R algorithm is derived. The reduction of the computational complexity for the ICA-R algorithm is achieved through (1) pre-whitening the observed signals; and (2) normalizing the weight vector. Computer simulations were performed on synthesized signals, a speech signal, and electrocardiograms (ECG). Results of these analyses demonstrate the efficiency and accuracy of the proposed algorithm.