Sparse Component Analysis in Presence of Noise Using an Iterative EM-MAP Algorithm

Hadi Zayyani (1) , Massoud Babaie-Zadeh (1) , G. Hosein Mohimani (1) , Christian Jutten (2)

1 SUT - Multimedia Lab.
2 GIPSA-SIGMAPHY - GIPSA - Signal Images Physique

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.

Keywords: sparse component analysis; sparse decomposition; blind source separation; independent component analysis

Domains: Signal and Image Processing; Signal and Image processing

Hadi Zayyani, Massoud Babaie-Zadeh, G. Hosein Mohimani, Christian Jutten. Sparse Component Analysis in Presence of Noise Using an Iterative EM-MAP Algorithm. ICA 2007 - 7th International Conference on Independent Component Analysis and Signal Separation, Sep 2007, London, United Kingdom. pp.438-445. ⟨hal-00173379⟩