A multi-stage framework for Dantzig selector and LASSO
The Journal of Machine Learning Research
Journal of Approximation Theory
Local appearance based robust tracking via sparse representation
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
The L1 penalized LAD estimator for high dimensional linear regression
Journal of Multivariate Analysis
Compressed Sensing via Dimension Spread in Dimension-Restricted Systems
Wireless Personal Communications: An International Journal
Detection of sparse targets with structurally perturbed echo dictionaries
Digital Signal Processing
Variable selection in high-dimension with random designs and orthogonal matching pursuit
The Journal of Machine Learning Research
| Hi-index | 754.84 |
We consider the orthogonal matching pursuit (OMP) algorithm for the recovery of a high-dimensional sparse signal based on a small number of noisy linear measurements. OMP is an iterative greedy algorithm that selects at each step the column, which is most correlated with the current residuals. In this paper, we present a fully data driven OMP algorithm with explicit stopping rules. It is shown that under conditions on the mutual incoherence and the minimum magnitude of the nonzero components of the signal, the support of the signal can be recovered exactly by the OMP algorithm with high probability. In addition, we also consider the problem of identifying significant components in the case where some of the nonzero components are possibly small. It is shown that in this case the OMP algorithm will still select all the significant components before possibly selecting incorrect ones. Moreover, with modified stopping rules, the OMP algorithm can ensure that no zero components are selected.