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2008

Greedy Signal Recovery Review

Needell, D., Tropp, J. A., Vershynin, R.

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Understand

The two major approaches to sparse recovery are L1-minimization and greedy methods.

Recently, Needell and Vershynin developed Regularized Orthogonal Matching Pursuit (ROMP) that has bridged the gap between these two approaches.
ROMP is the first stable greedy algorithm providing uniform guarantees.
Even more recently, Needell and Tropp developed the stable greedy algorithm Compressive Sampling Matching Pursuit (CoSaMP).

Greedy Signal Recovery Review · Around

Built on

Uncertainty principles and signal recovery
D. L. Donoho and P. B. Stark · 1989
Earlier work this paper cites.
Numerical Methods for Least Squares Problems
Å. Björck · 1996
Earlier work this paper cites.
Decoding by linear programming
E. Candès and T. Tao · 2005
Earlier work this paper cites.
Compressive sampling
E. Candès · 2006
Earlier work this paper cites.
Stable signal recovery from incomplete and inaccurate measurements
E. Candès, J. Romberg, and T. Tao · 2006
Earlier work this paper cites.

Similar

Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit
D. Needell and R. Vershynin · 2007
Cited alongside, same era.
Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit
D. Needell and R. Vershynin · 2007
Cited alongside, same era.
Signal recovery from random measurements via orthogonal matching pursuit
J. A. Tropp and A. C. Gilbert · 2007
Cited alongside, same era.
The restricted isometry property and its implications for compressed sensing
E. J. Candès · 2008
Cited alongside, same era.
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
D. Needell and J. A. Tropp · 2008
Cited alongside, same era.

Then

CoSaMP: Iterative signal recovery from noisy samples
D. Needell and J. A. Tropp · 2008
Closest in time.
On the impossibility of uniform sparse reconstruction using greedy methods
H. Rauhut · 2008
Closest in time.
On sparse reconstruction from Fourier and Gaussian measurements
M. Rudelson and R. Vershynin · 2008
Closest in time.
Uniform uncertainty principle for Bernoulli and subgaussian ensembles
S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann · 2009
Closest in time.

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