I came across a fascinating article on a new field in mathematics called compressed sensing. What it does, in a nutshell, is fill in missing data, and it does so astonishingly well.
It can take a noisy picture and filter away that noise in successive iterations, leaving you with a clear, sharp image. Far beyond what you might think is possible, even using fractal technology.
CS can also take a low resolution image and add resolution. While that statement may be technically inaccurate, to our eyes, that's what it does.
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