On the convergence of the affine scaling algorithm
Mathematical Programming: Series A and B
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Approximation of functions over redundant dictionaries using coherence
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Exact Regularization of Convex Programs
SIAM Journal on Optimization
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
A generalized uncertainty principle and sparse representation in pairs of bases
IEEE Transactions on Information Theory
Sparse representations in unions of bases
IEEE Transactions on Information Theory
On sparse representations in arbitrary redundant bases
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Recovery of exact sparse representations in the presence of bounded noise
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
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Receive signal enhancement in MIMO eigenmode transmission system via sparse approximation
WiCOM'09 Proceedings of the 5th International Conference on Wireless communications, networking and mobile computing
Stable recovery of sparse signals and an oracle inequality
IEEE Transactions on Information Theory
Improved stability conditions of BOGA for noisy block-sparse signals
Signal Processing
Accelerated Block-coordinate Relaxation for Regularized Optimization
SIAM Journal on Optimization
Hi-index | 754.90 |
Sparse overcomplete representations have attracted much interest recently for their applications to signal processing. In a recent work, Donoho, Elad, and Temlyakov (2006) showed that, assuming sufficient sparsity of the ideal underlying signal and approximate orthogonality of the overcomplete dictionary, the sparsest representation can be found, at least approximately if not exactly, by either an orthogonal greedy algorithm or by l1-norm minimization subject to a noise tolerance constraint. In this paper, we sharpen the approximation bounds under more relaxed conditions. We also derive analogous results for a stepwise projection algorithm.