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

Abstract. In this paper, a new algorithm for source recovery in underdetermined 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 Mstep. The solution obtained by the proposed algorithm is compared to the minimum 1 -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.

• Type: Conference
• Year: 2007
• Where: ICA
• Authors: Hadi Zayyani, Massoud Babaie-Zadeh, G. Hosein Mohimani, Christian Jutten
• Keywords: Additive Gaussian Noise, Algorithm, ICA 2007, Signal Processing, Underdetermined Sparse Component