Blind Source Separation (BSS) is a well known approach for separating mixtures assuming no information besides the linearity of the source pictures combination.
Abstract
Blind Source Separation (BSS) is a well known approach for separating mixtures assuming no information besides the linearity of the source pictures combination.The method being used for the separation is transforming the mixtures to sparse mixtures using Wavelets Packets or blocks division. Choosing the best sparsed nodes or blocks according to well defined criteria. Comparing the results to other methods. Finally, testing the algorithm on real mixtures.
The problem
While looking outside the window of an illuminated room at night, you will probably see not only the view outside but also the reflections of objects in the room. This is an example to the general problem we are dealing with in this project – separating two mixtures where the only information given is that there is correlation between the mixtures.Each mixture was formed by linear combination of reflected light from a picture and light that is reflected from the glass.
The solution
Transforming the mixtures into sparsed pictures using either Wavelets Packets or blocks division. Choosing the best blocks or nodes according to criteria:Threshold, First Norm and Entropy (according to Shannon).Forming a Scatter Plot of the best sparsed nodes or blocks of both mixtures.Using Angle Histogram Pick Detection in order to find the main angles and comparing this method to BiModalFit. Finding the proportions between the source pictures using arctan of the found angles.Finding the inverse mixing matrix and multiplying the mixtures with this matrix. Comparing this method to INFOMAX.
Figure 1 – Block diagram of the project
Figure 2 –
Real mixtures (up right and up left)
Separated pictures using blocks division and First Norm criterion (down right and left)
Tools
Programming in Matlab 6 and using apptications of INFOMAX.
The real mixtures were photographed,using a linear polorizer.
Conclusions
It can be concluded from the simulation that the optimal method to separate two mixtures is by using INFOMAX (after Pre-Processing). The optimal criterion varied between the different methods:using blocks division the best criterion was First Norm, using Wavelets Packets the best criterion was Threshold & using INFOMAX (with Wavelets Packets as Pre-Processing) the best criterion was Entropy. However,when separating real mixtures we saw that the optimal method of separation is by blocks division using First Norm criterion. These two conclusions seem to contradicte each other. However, when using the algorithm on one pair of mixtures one can’t reach absolute conclusions.
We saw that using INFOMAX after some sort of Pre-Processing significally improved the results, compared to using INFOMAX without any Pre-Processing.
When restoring noisy mixtures, no method showed better results.
Acknowledgment
We would like to thank from the bottom of our heart to our projects supervisors Alex and Michael Bronstein and Dr. Michael Zibulevsky for their great ideas and the lab staff for all their help and support. We would also like to thank Hany Farid (Dartmouth College) for providing real mixtures. We are also grateful to the Ollendorf Minerva Center Fund for supporting this project.
Most of all we would like to thank our soulmates Boaz & Dror for their endless understanding, love and devotion.