1. Separation of Convolutive Image Mixtures Technion, Dept. EE Yoav Y. Schechner Joint studies with: Nahum Kiryati & Ronen Basri; Sarit Shwartz & Michael Zibulevsky 1

2. Separation of Convolved Images window camera 35 Schechner, Kiryati & Basri, Separation of transparent layers using focus

3. “far” scene camera “close” scene Convolutive Mixture 36 Schechner, Kiryati & Basri, Separation of transparent layers using focus

4. Optical Sectioning (microscopy) objects in spaceraw frames 37

5. Transparent Layers For each frequency Instabilities as Problematic at low frequencies Schechner, Kiryati & Basri, Separation of transparent layers using focus

6. Processed images l far l close Acquired images raw far raw close Schechner, Kiryati & Basri, Separation of transparent layers using focus

7. W separate A mix Independent Sources Linear Mixture Unknown Known Blind Source Separation

8. A mix & blur Convolutive Mixtures Shwartz, Schechner & Zibulevsky, Convolutive Mixtures 41

9. Separation Optimization W separate Shwartz, Schechner & Zibulevsky, Convolutive Mixtures

10. Mutual Information of a Convolutive Mixture W separate A mix & blur Shwartz, Schechner & Zibulevsky, Convolutive Mixtures

11. Separation in the Frequency Domain FFT Shwartz, Schechner & Zibulevsky, Convolutive Mixtures

12. Problem: No Statistic Ensemble in FT No statistics per frequency Shwartz, Schechner & Zibulevsky, Convolutive Mixtures

13. Separation by Sub-band Images Shwartz, Schechner & Zibulevsky, Convolutive Mixtures 43

14. Image Statistics * See for example: Simoncelli (99)

15. MI of Sparse Sources Parametric PDF MI is not convex in MI is convex in

16. Scale & Sign Ambiguity Shwartz, Schechner & Zibulevsky, Convolutive Mixture 44 transform inverse transform … imbalance

17. Permutation Ambiguity Shwartz, Schechner & Zibulevsky, Convolutive Mixture 45 transform inverse transform inverse … crosstalk

18. Out of Focus Blur See for example: Stokseth (69), Born; Wolf (70), Hecht (87), Mahajan (94), Braat; Dirksen; Janssen (02), Sheppard; Cooper (04).

19. Parametric Model for Blur Shwartz, Schechner & Zibulevsky, Convolutive Mixtures 46

20. Parametric Model for the Blur

21. Simulations of Natural Images

22. Simulation Blind Estimation Using Ideal kernel + 1% noise Shwartz, Schechner & Zibulevsky, Convolutive Mixtures 47

23. Experiment Raw images High-pass of raw images Separation results Shwartz, Schechner & Zibulevsky, Convolutive Mixtures 48