Better Photos Through Math

Wired magazine’s Jordan Ellenberg recently published an interesting piece about math. (So far, this does not pertain to photography, I know, but trust me—it will.) The story was based on the sparsity principle, which is a mathematical concept that states… well, I don’t exactly understand what it states. But some other smart people do, and this sparsity thingamajig led to the scientific field of compressed sensing. Again, some stuff I don’t understand happens here involving magnetic resonance imaging and… voila, higher-resolution photographs. Okay, I know I skipped some crucial details. Let me try to fill in the blanks in laymen’s terms. Actually, “filling in the blanks” might be a good way to explain what this process does.

The smart math and science and computer people who work in this field implement an algorithm to fill in the gaps in a low resolution “data set” (a digital image file, a low-quality audio recording, etc) by making better guesses (based on the scarcity principle) at what data should fill in the holes. It’s like interpolation, but without the stigma. And it apparently works really, really well.

This breakthrough does not mean that tomorrow you’ll be able to go out and get your Scarcity Principle plug-in for Photoshop, but perhaps in the coming years you’ll be able to up-res your image files in a much cleaner, higher quality way. Perhaps even someday you’ll be able to enlarge low-resolution video and still images the way they do in movies and TV shows—you know, when the cops are cleaning up surveillance footage to see in crystal clear detail who the bad guy really is. Maybe that will remain the stuff of science fiction, but it will still be great if we will just be able to make really big, really beautiful prints. Either way it’s a technology to keep an eye on, even if you don’t understand exactly how it works. (Once you’ve read the Wired story, for a little more insight into what photographers with a bit of math aptitude think about the concept as it applies to digital imaging, head over to and check out the scarcity principle discussion forum.)

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