Fueling Innovation and Discovery The Mathematical Sciences in the 21st Century (2012) / Chapter Skim
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Compressed Sensing / Through the Kaleidoscope
Compressed Sensing / Through the Kaleidoscope
Pages 3-6
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From page 3... ...
. There are coarse wavelets for identifying general features and fine wavelets for identifying particular details.
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at a decent resolution, and they are not ideal for imaging patients such as children, who are unable to hold still and might not be good candidates for sedation. These challenges led to the discovery that MRI test images could, under certain conditions, be reconstructed perfectly -- not approximately, but perfectly -- from a too-short scan by a mathematical method called L1 (read as "ell one")
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From page 5... ...
Wavelets allow computers to compress an image into a smaller data file. Subdivision surfaces do the reverse: They allow the computer to create a small data file that can be manipulated and then uncompressed to create lifelike images of something that never existed -- in this case, an old man playing chess in the park.
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From page 6... ...
L1 minimization happens to be a good technique for zeroing in on that one sparse solution. Compressed sensing actually built on, and helped make coherent, ideas that had been applied or developed in particular scientific contexts, such as geophysical imaging and theoretical computer science, and even in mathematics itself (e.g., geometric functional analysis)
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