Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Foundations of Computational Mathematics
Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
Foundations of Computational Mathematics
High-resolution radar via compressed sensing
IEEE Transactions on Signal Processing
Subspace pursuit for compressive sensing signal reconstruction
IEEE Transactions on Information Theory
On recovery of sparse signals via l1 minimization
IEEE Transactions on Information Theory
Compressive Sensing by Random Convolution
SIAM Journal on Imaging Sciences
Shifting inequality and recovery of sparse signals
IEEE Transactions on Signal Processing
Analysis of orthogonal matching pursuit using the restricted isometry property
IEEE Transactions on Information Theory
Coherence-based performance guarantees for estimating a sparse vector under random noise
IEEE Transactions on Signal Processing
The Gelfand widths of lp-balls for 0
Journal of Complexity
Performance analysis for sparse support recovery
IEEE Transactions on Information Theory
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Stability Results for Random Sampling of Sparse Trigonometric Polynomials
IEEE Transactions on Information Theory
Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise
IEEE Transactions on Information Theory
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This article considers nonuniform support recovery via Orthogonal Matching Pursuit (OMP) from noisy random measurements. Given m admissible random measurements (of which Subgaussian measurements is a special case) of a fixed s-sparse signal x in R^n corrupted with additive noise, we show that under a condition on the minimum magnitude of the nonzero components of x, OMP can recover the support of x exactly after s iterations with overwhelming probability provided that m=O(slogn). This extends the results of Tropp and Gilbert (2007) [53] to the case with noise. It is a real improvement over previous results in the noisy case, which are based on mutual incoherence property or restricted isometry property analysis and require O(s^2logn) random measurements. In addition, this article also considers sparse recovery from noisy random frequency measurements via OMP. Similar results can be obtained for the partial random Fourier matrix via OMP provided that m=O(s(s+log(n-s))). Thus, for some special cases, this answers the open question raised by Kunis and Rauhut (2008) [34], and Tropp and Gilbert (2007) [53].