Revisiting sparse ICA from a synthesis point of view: Blind Source Separation for over and underdetermined mixtures

This paper studies the existing links between two approaches of Independent Component Analysis (ICA) - FastICA/projection pursuit and Infomax/Maximum likelihood estimation - and the Sparse Component Analysis (SCA), to tackle Blind Source Separation (BSS) of the instantaneous mixtures problem. While ICA methods suit particularly well for (over)determined and noiseless mixtures, SCA has demonstrated its robustness to noise and its ability to deal with underdetermined mixtures. Using the “synthesis” point of view to reformulate ICA methods as an optimization problem, we propose a new optimization framework, which encompasses both approaches. We show that the algorithms developed to minimize the proposed functional built on SCA, but imposing a numerical decorrelation constraint on the sources, aims to improve the Signal to Inference Ratio (SIR) of the estimated sources without degrading the Signal to Distortion Ratio (SDR).