The information maximization (Infomax) based on information entropy theory is a class of methods that can be used to blindly separate the sources. Torkkola applied the Infomax criterion to blindly separate the mixtures where the sources have been delayed with respect to each other. Compared to the frequency domain methods, this time domain method has simple adaptation rules and can be easily implemented. However, Torkkola's method works only in the real valued field. In this letter, the Infomax for blind separation of the delayed sources is extended to the complex case for processing of complex valued signals. Firstly, based on the gradient ascent the adaptation rules for the parameters of the unmixing network are derived and the steps of algorithm are given. Then, a measurement matrix is constructed to evaluate the separation performance. The results of computer experiment support the extended algorithm.

Fetal electrocardiogram (FECG) extraction is of vital importance in biomedical signal processing. A promising approach is blind source extraction (BSE) emerging from the neural network fields, which is generally implemented in a semi-blind way. In this paper, we propose a robust extraction algorithm that can extract the clear FECG as the first extracted signal. The algorithm exploits the fact that the FECG signal's kurtosis value lies in a specific range, while the kurtosis values of other unwanted signals do not belong to this range. Moreover, the algorithm is very robust to outliers and its robustness is theoretically analyzed and is confirmed by simulation. In addition, the algorithm can work well in some adverse situations when the kurtosis values of some source signals are very close to each other. The above reasons mean that the algorithm is an appealing method which obtains an accurate and reliable FECG.

In this study, we propose a robust approach for blind source separation (BSS) by using radial basis function networks (RBFNs) and higher-order statistics (HOS). The RBFN is employed to estimate the inverse of a hypothetical complicated mixing procedure. It transforms the observed signals into high-dimensional space, in which one can simply separate the transformed signals by using a cost function. Recently, Tan et al. proposed a nonlinear BSS method, in which higher-order moments between source signals and observations are matched in the cost function. However, it has a strict restriction that it requires the higher-order statistics of sources to be known. We propose a cost function that consists of higher-order cumulants and the second-order moment of signals to remove the constraint. The proposed approach has the capacity of not only recovering the complicated mixed signals, but also reducing noise from observed signals. Simulation results demonstrate the validity of the proposed approach. Moreover, a result of application to X-ray image separation also shows its practical applicability.