Recovering Data From Noise 206
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."
Re:Demo image (Score:5, Informative)
indeed. check the caption :
"Photos: Obama: Corbis; Image Simulation: Jarvis Haupt/Robert Nowak" (emphasis added by me)
Re:Why not... (Score:4, Informative)
(a) JPEG doesn't know either
JPEG is built on the assumption that the higher frequency components are less important, so it spends less bits on representing those components than it does on the lower frequency ones.
It's a pretty crude model (not least because of the block based architecture that makes it simple to implement but introduces artifacts at block boundries) but it still does a lot better than just throwing away pixels and/or reducing the bits per pixel in the original image.
Re:Why not... (Score:1, Informative)
You have to understand that the digital camera example is a toy example, i.e., the theory works beautifully but it has little use in practice (in this particular configuration). The other example that is mentioned in the article (MRI) better showcases the advantages of CS. When it takes about 200s to take a full acquisition of the image, you can take much fewer measurements in ~40s and then reconstruct the image using a CS algorithm. There are other examples where using CS brings similar advantages in practice; mostly when acquiring a single measurement is either expensive or takes a long time.
Re:Demo image (Score:3, Informative)
"Image Simulation" likely means that they simulated the acquisition. The recovery of the "after" image from the "before" image is probably as shown, it's just that the "before" image was not acquired from an actual camera. Those results don't look particularly amazing for compressed sensing. See this for example [robbtech.com].
Image stacking (Score:4, Informative)
After cropping, I may end up with a 1-2 megapixel image (sometimes much lower)
Try image stacking. A program I've used successfully for this is PhotoAcute. Provided your body+lens combo is in their database, you can stack multiple near-identical images (use Burst or Auto-bracket mode) and get "super resolution". Of course, this doesn't work so well if your subject is moving. If your body+lens combo isn't in their database, you can volunteer a couple hours of your time to make a set of ~ 100 specific images they can use to create a profile for your gear. If they accept it, they'll offer you a free license for the software. I have no connection with the company other than being a satisfied customer.
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.nosig