On sparse reconstruction from Fourier and Gaussian measurements

@inproceedings{Rudelson2008OnSR,
  title={On sparse reconstruction from Fourier and Gaussian measurements},
  author={Mark Rudelson and Roman Vershynin},
  year={2008}
}
This paper improves upon best-known guarantees for exact reconstruction of a sparse signal f from a small universal sample of Fourier measurements. The method for reconstruction that has recently gained momentum in the sparse approximation theory is to relax this highly nonconvex problem to a convex problem and then solve it as a linear program. We show that there exists a set of frequencies Ω such that one can exactly reconstruct every r-sparse signal f of length n from its frequencies in… CONTINUE READING
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