A simple test to check the optimality of a sparse signal approximation
Signal Processing - Sparse approximations in signal and image processing
Improved FOCUSS method with conjugate gradient iterations
IEEE Transactions on Signal Processing
A plurality of sparse representations is better than the sparsest one alone
IEEE Transactions on Information Theory
On the stable recovery of the sparsest overcomplete representations in presence of noise
IEEE Transactions on Signal Processing
Non-negative sparse decomposition based on constrained smoothed ℓ0 norm
Signal Processing
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Certain sparse signal reconstruction problems have been shown to have unique solutions when the signal is known to have an exact sparse representation. This result is extended to provide bounds on the reconstruction error when the signal has been corrupted by noise or is not exactly sparse for some other reason. Uniqueness is found to be extremely unstable for a number of common dictionaries.