# 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} }

- Published 2008
DOI:10.1002/cpa.20227

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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