Everybody knows the effect of pixelated objects (e.g. faces) on TV. Is there a way - and which mathematical method lies behind it - to un-pixelate the region? Beware: I am not talking about smoothing it out (unblur) image by image - but about using the information of a whole sequence of pixelated pictures where the object which is pixelated naturally changes the location within the overall pixelated region. I guess it must be some kind of "un-averaging over time" (e.g. differentiation over time comes into mind).

Has anybody tackled this problem yet? Are there references, demos, software...?

Thank you.

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    $\begingroup$ Offtopic ? $\endgroup$ – Qfwfq Jan 10 '11 at 15:03
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    $\begingroup$ @unknowngoogle: No, I don't think so because the underlying math should not be trivial. $\endgroup$ – vonjd Jan 10 '11 at 15:04
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    $\begingroup$ Sounds extremely hard to do. To do that, you should first obtain some information on how the pixelated object moves in successive frame. And that is a difficult problem in itself, even on plain un-pixelated images. $\endgroup$ – Federico Poloni Jan 10 '11 at 15:20
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    $\begingroup$ @unknowngogle: Yes, it does sound like a question in applied math, doesn't it? I don't think it makes it not research-level or unsuitable for MO, though. $\endgroup$ – Thierry Zell Jan 10 '11 at 16:34
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    $\begingroup$ You might also try the astronomy literature --- all the time they deal with point sources being pixelated. It's been a long time since I was an astronomer, so I don't have any references for you, sadly. $\endgroup$ – Scott Morrison Jan 11 '11 at 21:47

This is a problem that has been addressed by the computer vision community in the past few years. You may want to look into upsampling and super-resolution techniques as well as vectorization methods. Here is a recent paper on the topic in ICCV 2009 which gives a good summary of the recent efforts in this field: http://www.wisdom.weizmann.ac.il/~vision/SingleImageSR.html

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    $\begingroup$ This is extremely helpful - now I have the keywords for finding out more - obviously there is some high-level research going here - Thank you! $\endgroup$ – vonjd Jan 10 '11 at 15:29

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