Blind Source Separation

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 is being used for separation of mixtures photographed from a short distance (perspective projection). Forming the mixtures matrix using the geometry of the problem and the simulator equations. Dividing the mixtures to blocks enables assuming that locally one can use the algorithm of the former project which deals with orthographic projection. The algorithm includes transforming the blocks to sparse ones. Interpolation is being used to achieve full restoration. Finally, testing the algorithm on real source pictures.
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 the light that is reflected from the glass.

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Figure 1 -Real Source Pictures
The solution
Dividing the mixtures to basis blocks (different divisions were examined). Transforming the blocks into sparsed ones using either inner blocks division or Wavelets Packets. Choosing the best inner blocks or nodes according to criterions: Threshold, First Norm and Entropy (according to Shannon). Forming a Scatter Plot for the best blocks (nodes) of both mixtures, for each block. Using Angle Histogram Peak Detection in order to find the main angles. Forming two angle matrices and extending them by using interpolation (linear or cubic). Finding the proportions of the mixture matrix by using arctan of the found angles. Finding the inverse mixing matrix and multiplying the mixtures with this matrix. Comparing to restoration achieved by using initial dilution of the basis blocks.

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Figure 2 -Project Algorithm

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Figure 3 – Tendencies of Restoration
Conclusions
It can be concluded from the simulation that by using the former algorithm on the basis blocks two effects have been achieved: approximation to the picture curvature and loosing information.These effects contradict each other and eventually the second one is the dominant one.
It can be seen that dividing the mixtures to local blocks causes to a decrease (via the focal length) in the quality of the restored pictures which is much more monotonous, compare to using the algorithm on the whole mixtures whereas a sharp decrease is observed.
However, results obtained when dividing the mixtures to blocks are much worse than results obtained when using the algorithm on the whole mixtures. This phenomenan is caused by a few factors:finding the angles by using the angle histogram depends on parameters which are experimental defined per one Scatter Plot so using more than one base block results in loosing control over the parameters, using linear interpolation rather then cubic interpolation involves an increase in the interpolation error but using cubic interpolation dealing with 16 blocks is meaningless. Besides, dividing to many blocks such as 256 blocks might cause, in case one picture is much more dominant than the second one, loosing information of the less dominant picture.
It can be concluded that fundamentally the motivation to restoring pictures from mixtures photographed using perspective projection is positive but more accurate restoration ways must be find first.

Acknowledgments
I would like to thank my project supervisors Alex and Michael Bronstein and Dr. Michael Zibulevsky for their help and guidance throughout this work.
I am also grateful to the Ollendorff Minerva Center Fund for supporting this project.
Most of all I would like to thank my soulmate Dror for his endless understanding, love and devotion.