Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information

  title={Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information},
  author={Emmanuel J. Cand{\`e}s and Justin K. Romberg and Terence Tao},
  journal={IEEE Transactions on Information Theory},
This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f/spl isin/C/sup N/ and a randomly chosen set of frequencies /spl Omega/. Is it possible to reconstruct f from the partial knowledge of its Fourier coefficients on the set /spl Omega/? A typical result of this paper is as follows. Suppose that f is a superposition of |T| spikes f(t)=/spl sigma//sub /spl tau//spl isin/T/f(/spl tau/)/spl delta/(t-/spl tau/) obeying… 

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