alt Hacker NewsDo you have any good reference for compressed sensing?
The high level description on wikipedia seems very compelling.. And would you say it'd be a huge task to really grok it?
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ghtbircshotbe • last Monday at 12:37 PM
Article by Terrence Tao: https://terrytao.wordpress.com/2007/04/13/compressed-sensing...
Paper by Stan Osher et al: https://arxiv.org/abs/1104.0262
A while back I looked at matching pursuit. At first it seemed very complicated, but after staring at it a bit realized it's simple.
- Start with a list of basis functions and your signal.
- Go through the list and find the basis function that best correlates with the signal. This gives you a basis function and a coefficient.
- Subtract out the basis function (scaled by the coefficient) from your signal, and then repeat with this new residual signal.
The Fourier transform is similar using sine wave basis functions.
The key that makes this work in situations where the Nyquist theorem says we don't have a high enough sampling rate is ensuring our sampling (possibly random) is un-correlated with the basis functions and our basis functions are good approximations for the signal. That lowers the likelihood that our basis functions correlating well with our samples is by chance and raises likelihood it correlates well with the actual signal.