Independent Component Analysis Based on Non-polynomial Approximation of Negentropy: Application to MRS Source Separation

In this paper, a new ICA algorithm based on non-polynomial approximation of negentropy that captures both the asymmetry of the sources’ PDF and the $sub/super$-Gaussianity of this latter is proposed. A gradient-ascent iteration with quasi-optimal stepsize is used to maximize the considered cost function. With this quasi-optimal computation in the case of highly non-linear objective function, the main advantages of the proposed algorithm are 1) its robustness to outliers compared to kurtosis-based ICA method especially for situations of small data size, and 2) its ability to capture sources’ asymmetric probability density functions which is a property that can’t be fulfilled in classic ICA algorithms like FastICA. Numerical results reported in the context of source separation of brain magnetic resonance spectroscopy show the superiority of the proposed algorithm over the FastICA algorithm in terms of both source separation accuracy and the number of iterations required for convergence.