Blind Source Separation using mixtures scatter plot properties

The scatter plot of two image mixtures, generated by mixing two positive sources, is bounded by a parallelogram, the orientations of which are defined by the two ratios of the four mixing coefficients. The existence of inter-source dependencies creates a distribution bounded by a different rectilinear shape, bounded by the original parallelogram. Based on this observations a robust graphical method for Blind Source Separation (BSS) is presented with reference to the scatter plot of the mixtures. The error analysis in presence of inter source dependencies is presented.

[1]  Jean-François Cardoso,et al.  Multidimensional independent component analysis , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[2]  Barak A. Pearlmutter,et al.  Independent Component Analysis: Blind source separation by sparse decomposition in a signal dictionary , 2001 .

[3]  Peter J. Rousseeuw,et al.  Robust Regression and Outlier Detection , 2005, Wiley Series in Probability and Statistics.

[4]  Yehoshua Y. Zeevi,et al.  Sparse ICA for blind separation of transmitted and reflected images , 2005, Int. J. Imaging Syst. Technol..

[5]  Wolfgang Härdle,et al.  Robust and nonlinear time series analysis : proceedings of a workshop organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983 , 1984 .

[6]  Barak A. Pearlmutter,et al.  Blind Source Separation by Sparse Decomposition in a Signal Dictionary , 2001, Neural Computation.

[7]  Kang Li,et al.  Semantics-Based Video Indexing using a Stochastic Modeling Approach , 2007, 2007 IEEE International Conference on Image Processing.

[8]  Barak A. Pearlmutter,et al.  Blind source separation by sparse decomposition , 2000, SPIE Defense + Commercial Sensing.

[9]  Pavel Kisilev,et al.  Multiscale Framework For Blind Source Separation , 2003 .

[10]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[11]  Yehoshua Y. Zeevi,et al.  A Multiscale Framework For Blind Separation of Linearly Mixed Signals , 2003, J. Mach. Learn. Res..

[12]  Yehoshua Y. Zeevi,et al.  Separation of reflections via sparse ICA , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).