Risk-averting cost function for Independent Component Analysis in signals with multiplicative noise

The FMICA is a method to extract the mixture of independent sources when they are contaminated with multiplicative noise, and notably improves the standard ICA methods in the presence of this kind of noise, although its results worsen when the level of noise increases. In this paper, whether this worsening is due to the existence of local minima or problems in the convergence of the statistical functions used is studied by a modification in the cost function that appears in FMICA. This new cost function has the property that, asymptotically, it does not present local minima, so it provides insights on the global convergence of the original cost function and it leads to the improvement of the behaviour of the FMICA for high noise levels, increasing the applicability of the method.