Compressed sensing is a mathematical tool that creates hi-res data sets from lo-res samples. It can be used to resurrect old musical recordings, find enemy radio signals, and generate MRIs much more quickly.
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Compressed sensing works something like this: You’ve got a picture — of a kidney, of the president, doesn’t matter. The picture is made of 1 million pixels. In traditional imaging, that’s a million measurements you have to make. In compressed sensing, you measure only a small fraction — say, 100,000 pixels randomly selected from various parts of the image. From that starting point there is a gigantic, effectively infinite number of ways the remaining 900,000 pixels could be filled in.
The key to finding the single correct representation is a notion called sparsity, a mathematical way of describing an image’s complexity, or lack thereof. A picture made up of a few simple, understandable elements — like solid blocks of color or wiggly lines — is sparse; a screenful of random, chaotic dots is not. It turns out that out of all the bazillion possible reconstructions, the simplest, or sparsest, image is almost always the right one or very close to it.
In a nutshell: the simplest answer is right most of the time.
The thing is, teaching a computer this may seem simple, but it's huge. Being able to take 100,000 datapoints (not just pixels) and being able to accurately predict a million others, is MASSIVE. You could take an old recording, get rid of the pops and imperfections and, in theory, make it sounds as though you were really there. Who knows what could be predicted if we aimed this algorithm at the stars? Or at cancer?
....or at politics? The environment? Our DNA?
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