Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
Neural Computation
Fast sparse representation based on smoothed lo norm
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Underdetermined blind source separation based on sparse representation
IEEE Transactions on Signal Processing
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
An iterative Bayesian algorithm for sparse component analysis in presence of noise
IEEE Transactions on Signal Processing
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In this paper, a new algorithm for source recovery in under-determined Sparse Component Analysis (SCA) or atomic decomposition on over-complete dictionaries is presented in the noisy case. The algorithm is essentially a method for obtaining sufficiently sparse solutions of under-determined systems of linear equations with additive Gaussian noise. The method is based on iterative Expectation-Maximization of a Maximum A Posteriori estimation of sources (EM-MAP) and a new steepest-descent method is introduced for the optimization in the M-step. The solution obtained by the proposed algorithm is compared to the minimum l1-norm solution achieved by Linear Programming (LP). It is experimentally shown that the proposed algorithm is about one order of magnitude faster than the interior-point LP method, while providing better accuracy.