Blind Source Separation of image sources

The case of more sensors than sources

• 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.

  See the paper in Neural Network World 1996.

  

  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.

More sources than sensors (M < N)

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

See the paper on hiding images in other "carrier" images presented at ICPR 1996.

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

Correlated image sources

It can be observed that natural images, are similar to nonstationary signals and they usually are cross-correlated.

See the specifics of image separation in a paper presented at EUSIPCO 1996.

Example:

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

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