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Math Science

Recovering Data From Noise 206

Posted by kdawson
from the sparse-world-after-all dept.
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."
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Recovering Data From Noise

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  • CSI (Score:5, Funny)

    by fuzzyfuzzyfungus (1223518) on Tuesday March 02, 2010 @08:15AM (#31328740) Journal
    Enhance!
  • by jellomizer (103300) on Tuesday March 02, 2010 @08:56AM (#31329120)

    After applying the Noise filter to mess up my image I hit Undo and my image is back to normal.

  • Deckard (Score:1, Funny)

    by Anonymous Coward on Tuesday March 02, 2010 @09:02AM (#31329188)
    Enhance 34 to 36. Pan right and pull back. Stop. Enhance 34 to 46. Give me a hard copy right there.
  • by Chapter80 (926879) on Tuesday March 02, 2010 @09:27AM (#31329482)

    Here's how Compressed Sensing works with standard JPGs.

    First the program takes the target JPG (which you want to be very large), and treats it as random noise. Simply a field of random zeros and ones. Then, within that vast field, the program selects a pattern or frequency to look for variations in the noise pattern.

    The variations in the noise pattern act as a beacon - sort of a signal that the payload is coming. Common variations include mathematical pulses at predictable intervals - say something that would easily be recognizable by a 5th-grader, like say a pattern of prime numbers.

    Then it searches for a second layer, nested within the main signal. Some bits are bits to tell how to interpret the other bits. Use a gray scale with standard interpolation. Rotate the second layer 90 degrees. Make sure there's a string break every 60 characters, and search for an auxiliary sideband channel. Make sure that the second layer is zoomed out sufficiently, and using a less popular protocol language; otherwise it won't be easily recognizable upon first glance.

    Here's the magical part: It then finds a third layer. Sort of like in ancient times when parchment was in short supply people would write over old writing... it was called a palimpsest. Here you can uncompress over 10,000 "frames" of data, which can enhance a simple noise pattern to be a recognizable political figure.

    Further details on this method can be found here. [imsdb.com]

    --
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