Blind separation of sources (Independent Component Analysis)

• The Problem

  The task is to separate an unknown number N of unknown sources S from M measured linear mixtures of signals.

• Extended case: more sensors than sources (M > N)

  An additional layer was proposed for automatic elimination of redundancy among the separated signal set. For this layer an anti-Hebbian like learning rule was developed (Cichocki:Kasprzak:NNW96).

  

  Fig. 7 A two-layer neural network for source separation and redundancy elimination.

  An example for image sources if M=4, N=3:

  
  Three (unknown) original images

  
  Four mixtures of three sources

  
  Separated images after the first layer (two Susie images)

  
  Four output images after the redundancy elimination layer

  Fig. 8 Example of blind separation for more sensors than sources

  The above redundancy elimination process is demonstrated by following movie:

  MONOMPEG (660 kB).

• More sources than sensors (M < N):

  As this case constitutes an under-determined problem we have proposed an image encryption scheme (Kasprzak:Cichocki:ICPR96). on the basis of blind source separation (Fig. 9).

  

  Fig. 9 A secured image transmission on the basis of blind separation.

• Practical problem: natural images are correlated and similar to nonstationary signals

  It can be observed that natural images, after scanning them to 1-D signals, are similar to nonstationary signals and they usually are correlated one to each other.

  Example:

  

  Fig. 10 Three image sources - one natural and two synthetic images.

  

  

  

  Fig. 11 1-D sources after scanning the images from Fig. 10.

  Specific problems arising in blind separation of image sources are discussed in the paper (Cichocki:Kasprzak:Amari:Eusipco96).