Recovering Data From Noise

An anonymous reader tips an account up at Wired of a hot new field of mathematics and applied algorithm research called "compressed sensing" that takes advantage of the mathematical concept of sparsity to recreate images or other datasets from noisy, incomplete inputs. "[The inventor of CS, Emmanuel] Candès can envision a long list of applications based on what he and his colleagues have accomplished. He sees, for example, a future in which the technique is used in more than MRI machines. Digital cameras, he explains, gather huge amounts of information and then compress the images. But compression, at least if CS is available, is a gigantic waste. If your camera is going to record a vast amount of data only to throw away 90 percent of it when you compress, why not just save battery power and memory and record 90 percent less data in the first place? ... The ability to gather meaningful data from tiny samples of information is also enticing to the military."

Comments

Why not...

[jbb999]

If your camera is going to record a vast amount of data only to throw away 90 percent of it when you compress, why not just save battery power and memory and record 90 percent less data in the first place? ..

Because it's hard to know what is needed and what isn't to produce a photograph that still looks good to a human, and pushing that computing power down to the camera sensors where power is more limited than a computer is unlikely to save either time or power.

Re:Why not...

[Chrisq]

I think you are missing the point, throwing away 90% of the image was a demonstration of the capabilities of this algorithm. You would use it where you have only managed to capture a small amount of data, not capture the lot and throw away 90%.

Re:I am a bit worried about the "fill in the shape

[Yvanhoe]

Exactly. This algorithm doesn't create absent data nor does it infer it, it just makes the uncertainties it has "nicer" than the usual smoothing.

Not smoothing

[nten]

The article was a bit poor. The data sets aren't really incomplete in most cases. They only seem that way from a traditional standpoint. The missing samples often contain absolutely no information, in which case the original image/signal can be reconstructed perfectly. In brief, nyquist is a rule about sampling non-sparse data, so if you rotate your sparse data into a basis in which it is non-sparse, and you satisfy the nyquist rule in that basis (though not in the original one), you are still fine.

I like this link better l1 magic