SUT

J. Eriksson and V. Koivunen, "Complex-valued ICA using second order statistics," in Proc. IEEE Workshop on Machine Learning for Signal Processing (MLSP), Sao Luis, Brazil, pp. 183-192 , Sept. 2004.

Brief introduction:
Strong-uncorrelating transform (SUT) can be viewed as an extension of the conventional whitening transform for complex random vectors. For a complex random vector, after the SUT transform, its covariance matrix and pseudo-covariance matrix both will be diagonal. SUT can be used as one of complex ICA methods when the sources are all noncircular and with distinct noncircularity indices. When the sources are circular, SUT reduces to regular whitening transform.

Parameters of the algorithm:
X: mixtures

GUT

E. Ollila and V. Koivunen, "Complex ICA using generalized uncorrelating transform," IEEE Trans. on Signal Processing, vol. 89, no. 4, pp.365-377, 2006.

Brief introduction:
Generalized uncorrelating transform (GUT) is a generalization of the strong-uncorrelating transform based upon generalized estimators of the covariance and pseudo-covariance matrix, called the scatter matrix and spatial pseudo-scatter matrix, respectively. GUT is a separating matrix estimator for complex-valued ICA when at most one source random variable possesses circularly symmetric distribution and sources do not have identical distribution. GUT matrices that employed a pair of robust scatter and spatial pseudo-scatter matrix were unaffected by outliers whereas other estimators might fail to separate the sources.

Parameters of the algorithm:
X: mixtures
Type: to specify the scatter matrix and the spatial pseudo-scatter matrix used in the algorithm. The scatter matrices could be the general covariance and pseudo-covariance matrix, or the covariance matrix and pseudo-kurtosis matrix, or the covariance matrix and sign pseudo-covariance matrix.

SOBI

A. Belouchrani, K. Abed Meraim, J. F. Cardoso, and E. Moulines, "A blind source separation technique based on second order statistics," IEEE Trans. Signal Processing, vol. 45, no. 2, pp. 434 - 444, 1997.

ERM-G and ncSOBI

X.-L. Li and T. Adali, "Blind Separation of complex noncircular stationary Gaussian sources," IEEE Trans. Signal Processing, in review.

Brief introduction:
An entropy rate minimization (ERM) algorithm is introduced for the blind source separation of complex noncircular stationary Gaussian sources. A parametric entropy rate estimator that uses a widely linear autoregressive model for the sources is proposed. Minimizing the mutual information of separated time series yields the algorithm. The identification condition is also given in the paper. For sources with distinct correlation or relation functions, it is always possible to select a set of time delays such that the identification condition is satisfied.
Parameters of the algorithm:
X: mixtures
Tau1: a vector including the time delays for covariance matrices estimation
Tau2: a vector including the time delays for pseudo-covariance matrices estimation