Restricted isometry constants where lpsparse recovery can fail for 0
IEEE Transactions on Information Theory
On recovery of sparse signals via l1 minimization
IEEE Transactions on Information Theory
Shifting inequality and recovery of sparse signals
IEEE Transactions on Signal Processing
Stable recovery of sparse signals and an oracle inequality
IEEE Transactions on Information Theory
Uncertainty principles and ideal atomic decomposition
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
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Sparse Legendre expansions via l1-minimization
Journal of Approximation Theory
The L1 penalized LAD estimator for high dimensional linear regression
Journal of Multivariate Analysis
Hi-index | 754.84 |
This paper discusses new bounds for restricted isometry constants in compressed sensing. Let φ be an n×p real matrix and k be a positive integer with k ≤ n. One of the main results of this paper shows that if the restricted isometry constant δk of φ satisfies δk k-sparse signals are guaranteed to be recovered exactly via l1 minimization when no noise is present and k-sparse signals can be estimated stably in the noisy case. It is also shown that the bound cannot be substantially improved. An explicit example is constructed in which δk = k-1/2k-1 k-sparse signals.