Compressed sensing with cross validation
IEEE Transactions on Information Theory
Average case analysis of multichannel sparse recovery using convex relaxation
IEEE Transactions on Information Theory
Exact signal recovery from sparsely corrupted measurements through the pursuit of justice
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
$\ell_1$ Minimization with Noisy Data
SIAM Journal on Numerical Analysis
Restricted p---isometry property and its application for nonconvex compressive sensing
Advances in Computational Mathematics
| Hi-index | 0.12 |
In compressed sensing, we seek to gain information about a vector x∈ℝN from d ≪ N nonadaptive linear measurements. Candes, Donoho, Tao et al. (see, e.g., Candes, Proc. Intl. Congress Math., Madrid, 2006; Candes et al., Commun. Pure Appl. Math. 59:1207–1223, 2006; Donoho, IEEE Trans. Inf. Theory 52:1289–1306, 2006) proposed to seek a good approximation to x via ℓ 1 minimization. In this paper, we show that in the case of Gaussian measurements, ℓ 1 minimization recovers the signal well from inaccurate measurements, thus improving the result from Candes et al. (Commun. Pure Appl. Math. 59:1207–1223, 2006). We also show that this numerically friendly algorithm (see Candes et al., Commun. Pure Appl. Math. 59:1207–1223, 2006) with overwhelming probability recovers the signal with accuracy, comparable to the accuracy of the best k-term approximation in the Euclidean norm when k∼d/ln N.