Toeplitz-Structured Compressed Sensing Matrices
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
On recovery of sparse signals via l1 minimization
IEEE Transactions on Information Theory
A Frame Construction and a Universal Distortion Bound for Sparse Representations
IEEE Transactions on Signal Processing
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
Stable recovery of sparse signals and an oracle inequality
IEEE Transactions on Information Theory
New bounds for restricted isometry constants
IEEE Transactions on Information Theory
Rate Minimaxity of the Lasso and Dantzig Selector for the lq Loss in lr Balls
The Journal of Machine Learning Research
Phase transition in limiting distributions of coherence of high-dimensional random matrices
Journal of Multivariate Analysis
Hard Thresholding Pursuit: An Algorithm for Compressive Sensing
SIAM Journal on Numerical Analysis
A comparison of the lasso and marginal regression
The Journal of Machine Learning Research
Journal of Approximation Theory
The L1 penalized LAD estimator for high dimensional linear regression
Journal of Multivariate Analysis
Sparse matrix inversion with scaled Lasso
The Journal of Machine Learning Research
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In this paper, we present a concise and coherent analysis of the constrained l1 minimization method for stable recovering of high-dimensional sparse signals both in the noiseless case and noisy case. The analysis is surprisingly simple and elementary, while leads to strong results. In particular, it is shown that the sparse recovery problem can be solved via l1 minimization under weaker conditions than what is known in the literature. A key technical tool is an elementary inequality, called Shifting Inequality, which, for a given nonnegative decreasing sequence, bounds the l2 norm of a subsequence in terms of the l1 norm of another subsequence by shifting the elements to the upper end.