Abstract
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.
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Zayyani, H., Babaie-Zadeh, M., Mohimani, G.H., Jutten, C. (2007). Sparse Component Analysis in Presence of Noise Using an Iterative EM-MAP Algorithm. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds) Independent Component Analysis and Signal Separation. ICA 2007. Lecture Notes in Computer Science, vol 4666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74494-8_55
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DOI: https://doi.org/10.1007/978-3-540-74494-8_55
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