Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Learning Overcomplete Representations
Neural Computation
Method of optimal directions for frame design
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 05
Dictionary learning for sparse approximations with the majorization method
IEEE Transactions on Signal Processing
Probing the Pareto Frontier for Basis Pursuit Solutions
SIAM Journal on Scientific Computing
Parametric dictionary design for sparse coding
IEEE Transactions on Signal Processing
Dictionary learning for L1-exact sparse coding
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Dictionary identification: sparse matrix-factorization via l1-minimization
IEEE Transactions on Information Theory
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Sparse component analysis and blind source separation of underdetermined mixtures
IEEE Transactions on Neural Networks
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A new dictionary learning method for exact sparse representation is presented in this paper. As the dictionary learning methods often iteratively update the sparse coefficients and dictionary, when the approximation error is small or zero, algorithm convergence will be slow or non-existent. The proposed framework can be used in such a setting by gradually increasing the fidelity of the approximation. This technique has previously been used for the convex sparse representations. It has been extended here to the non-convex dictionary learning problem by allowing the dictionary be modified.