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

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Presentation transcript:

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

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

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

Optical Sectioning (microscopy) objects in spaceraw frames 37

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

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

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

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

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

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

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

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

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

Image Statistics * See for example: Simoncelli (99)

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

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

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

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

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

Parametric Model for the Blur

Simulations of Natural Images

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

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