Approximate Sparse Decomposition Based on Smoothed L0-Norm

Hamed Firouzi; Masoud Farivar; Massoud Babaie-Zadeh; Christian Jutten

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arXiv · 0811.2868

Approximate Sparse Decomposition Based on Smoothed L0-Norm

Hamed Firouzi·Masoud Farivar·Massoud Babaie-Zadeh·Christian Jutten

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Abstract

In this paper, we propose a method to address the problem of source estimation for Sparse Component Analysis (SCA) in the presence of additive noise. Our method is a generalization of a recently proposed method (SL0), which has the advantage of directly minimizing the L0-norm instead of L1-norm, while being very fast. SL0 is based on minimization of the smoothed L0-norm subject to As=x. In order to better estimate the source vector for noisy mixtures, we suggest then to remove the constraint As=x, by relaxing exact equality to an approximation (we call our method Smoothed L0-norm Denoising or SL0DN). The final result can then be obtained by minimization of a proper linear combination of the smoothed L0-norm and a cost function for the approximation. Experimental results emphasize on the significant enhancement of the modified method in noisy cases.

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Hamed Firouzi, Masoud Farivar, Massoud Babaie-Zadeh, Christian Jutten. 2008-11-18. Approximate Sparse Decomposition Based on Smoothed L0-Norm. https://arxiv.org/abs/0811.2868

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