March 1, 2010
Compressed sensing
An algorithm that resolves high resolution images from next to nothing.
Compressed sensing was discovered by chance. In February 2004, Emmanuel Candès was messing around on his computer, looking at an image called the Shepp-Logan Phantom. The image — a standard picture used by computer scientists and engineers to test imaging algorithms — resembles a Close Encounters alien doing a quizzical eyebrow lift. Candès, then a professor at Caltech, now at Stanford, was experimenting with a badly corrupted version of the phantom meant to simulate the noisy, fuzzy images you get when an MRI isn’t given enough time to complete a scan. Candès thought a mathematical technique called l1 minimization might help clean up the streaks a bit. He pressed a key and the algorithm went to work.
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CSI eat your heart out
From reading this, though, it seems their definition of “low resolution” is somewhat different than what is usually meant.
They are starting with very detailed images that are missing data, and are able to fill in the missing data with an algorithm that compares areas of missing data to neighboring “filled in” areas, which allow them to get a pretty good approximation of what should be used to fill in the missing pixels.
When I think of a low-res image, though, I think of, say, a 72-dpi line drawing of a building plan: in a high-res image there would, in a window for instance, be several adjacent line representing the sill, glass, sash, frame, etc., but in the low-res image there would just be a black blob, with no way of knowing the relationship between any of the adjacent lines, which have become too thick at low res to be individually represented.
That’s a more “everyday” example of low resolution and one that is not helped, as far as I can tell, by this technology.
“He pressed a key and the algorithm went to work.”
Was it the ‘Enhance’ key?
I just wrote something about Why Compressed Sensing is NOT a CSI “Enhance” technology … yet !
http://nuit-blanche.blogspot.com/2010/03/why-compressed-sensing-is-not-csi.html
Cheers,
Igor.