Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Breakdown of equivalence between the minimal l1-norm solution and the sparsest solution
Signal Processing - Sparse approximations in signal and image processing
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Linear programming in spectral estimation. Application to array processing
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 06
Direction finding of multiple emitters by spatial sparsity and linear programming
ISCIT'09 Proceedings of the 9th international conference on Communications and information technologies
A sparse signal reconstruction perspective for source localization with sensor arrays
IEEE Transactions on Signal Processing - Part II
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
On sparse representation in pairs of bases
IEEE Transactions on Information Theory
On sparse representations in arbitrary redundant bases
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
Time-frequency localization operators: a geometric phase space approach
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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We evaluate the accuracy of sparsity-based estimation methods inspired from compressed sensing. Typical estimation approaches consist of minimizing a non-convex cost function that exhibits local minima, and require excessive computational resources. A tractable alternative relies on a sparse representation of the observation vector using a large dictionary matrix and a convex cost function. This estimation approach converts the intractable high-dimensional non-convex problem into a simpler convex problem with reduced dimension. Unfortunately, the advantages come at the expense of increased estimation error. Therefore, an evaluation of the estimation error is of considerable interest. We consider the case of estimating a single parameter vector, and provide upper bounds on the achievable accuracy. The theoretical results are corroborated by simulations.