Independent component analysis based on marginal entropy approximations

The problem of blind source separation (BSS) can be solved through the statistical tool of independent component analysis (ICA). The present contribution reviews recent solutions to ICA contrasts based on the minimization of marginal entropy (ME). In the two-signal case, a novel estimator, so-called sinusoidal ICA (SICA), is obtained by approximating Comon´s 4th-order cumulant based contrast function. Interestingly, SICA as well as analogous methods scattered across the literature are particular instances of a class of closed-form solutions gathered under the name of general weighted estimator (GWE). In the n-dimensional case, n ≫ 2, these elementary estimators are applied over the input components in pairs, as in the Jacobi optimization (JO) technique for matrix diagonalization. The reduction of the computational burden of JO for ICA is addressed. Adaptive (on-line) versions are briefly considered as well. A simple simulation experiment illustrates the good performance of the approximate ME approach.