Real, Complex and Quaternion BSE and BSS, complex and quaternion noncircularity, improper signals

We have worked mostly on BSE based on some fundamental properties of sources, such as local predicability, smothness or sparsity, together with the separation of noisy and post-nonlinear mixtures. Applications of these algorithms are in automatic, EEG artifact removal for paradigms like Brain Computer INterface (BCI) or fatigue and microsleep detection in car drivers. We have also developed a class of widely linear, complex, and quaternion BSE and BSS algorithms. See below for our recent contributions in this field.

Legend: MATLAB code, PDF files, Supplements and data.

You can also download some EEG Data used in some of the simulations in the work below. The EEG data contain EOG and EMG artifacts coming from eye blinks, eyebrow raising and eye rolling, and are used in our BSE, BSS, and EMD algorithms. The recordings also contain a 50Hz power line noise. Enjoy!

Complex and quaternion valued BSS and BSE, widely linear model, augmented complex statistics, augmented CLMS, complex kurtosis, augmented quaternion statistics
  1. S. Javidi, D. P. Mandic, C. Cheong Took, and A. Cichocki, "Kurtosis Based Blind Source Extraction of Complex Noncircular Signals with Application in EEG Artifact Removal in Real Time", Frontiers in Neuroscience, vol. 5, no. 105, pp. 1–18, 2011. [pdf]
  2. S. Javidi, C. Cheong-Took, and D. P. Mandic, "A Fast Independent Component Analysis Algorithm for Quaternion Signals," IEEE Transactions on Neural Networks, vol. 22. no. 12, pp. 1967-1978, 2011. 10.pdf" title="download in PDF form">[pdf]
  3. S. Javidi, C. Cheong Took, C. Jahancahi, N. Le Bihan, and D. P. Mandic"Blind Extraction of Improper Quaternion Sources ," in Proceedings of ICASSP'11, pp. 3708-3711, 2011. [pdf]
  4. S. Javidi, D. P. Mandic, and A. Cichocki, "Complex Blind Source Extraction From Noisy Mixtures Using Second-Order Statistics," IEEE Transactions on Circuits and Systems I, vol. 57, no. 7, pp. 1404-1416, 2010. [pdf]
  5. M. G. Jafari, J. A. Chambers, and D. P. Mandic, "Natural Gradient Algorithm for Cyclostationary Sources," Electronic Letters, vol. 38, no. 14, pp. 758-759, 2002. [pdf]
Real BSS and BSE, noisy mixtures, post-nonlinear mixtures, adaptive step size
  1. D. P. Mandic and A. Cichocki, "An Online Algorithm for Blind Extraction of Sources with Different Dynamical Structures," 4th International Symposium on Independent Component Analysis and Blind Signal Separation (ICA2003), pp. 645-650, 2003. [pdf]
  2. W. Y. Leong and D. P. Mandic, "Post-Nonlinear Blind Extraction in the Presence of Ill-Conditioned Mixing," IEEE Transactions on Circuits and Systems I, vol. 55, no. 9, pp. 2631-2638, 2008. [pdf]
  3. W. Liu and D. P. Mandic, "A normalised kurtosis-based algorithm for blind source extraction from noisy measurements," Signal Processing, vol. 86, pp. 1580-1585, 2006. [pdf]
  4. W. Liu, D. P. Mandic, and A. Cichocki, "Blind Second-order Source Extraction of Instantaneous Noisy Mixtures, " IEEE Transactions on Circuits and Systems II, vol. 53, no. 9, pp. 931-935, 2006. [pdf]
  5. W. Y. Leong, W. Liu, and D. P. Mandic, "Blind source extraction: Standard approaches and extensions to noisy and post-nonlinear mixing," Neurocomputing, vol. 17, no. 10-12, pp. 2344-2355, 2008. [pdf]
  6. W. Liu, D. P. Mandic, and A. Cichocki,"Blind source extraction based on a linear predictor," IET Signal Processing, vol.1, no. 1, pp. 29-34, 2007. [pdf]
  7. W. Liu, D. P. Mandic, and A. Cichocki, "Analysis and Online Realization of the CCA Approach for Blind Source Separation," IEEE Transactions on Neural Networks, vol. 18, no. 5, pp. 1505-1510, 2007. [pdf]
  8. W. Leong, D. P. Mandic, and J. Chambers, "Blind Sequential Extraction of Ill-Conditioned Post-Nonlinearly Mixed Sources," Proceedings of the Nonlinear Statistical Signal Processing Workshop (NSSPW'06), Proc. on CD, 2006. [pdf]
  9. M. Jafari, J. Chambers, and D. P. Mandic,"A Novel Adaptive Learning Rate Sequential Blind Source Separation Algorithm," Signal Processing, vol. 84, pp. 801-804, 2004. [pdf]