  In a recent paper [4], Duarte and Jutten investigated the Blind Source
Separation (BSS) problem, for the nonlinear mixing model that they introduced
in that paper. They proposed to solve this problem by using
information-theoretic tools, more precisely by minimizing the mutual
information (MI) of the outputs of the separating structure. When applying the
MI approach to BSS problems, one usually determines the analytical expressions
of the derivatives of the MI with respect to the parameters of the considered
separating model. In the literature, these calculations were mainly reported
for linear mixtures up to now. They are more complex for nonlinear mixtures,
due to dependencies between the considered quantities. Moreover, the notations
commonly employed by the BSS community in such calculations may become
misleading when using them for nonlinear mixtures, due to the above-mentioned
dependencies. We claim that the calculations reported in [4] contain an error,
because they did not take into account all these dependencies. In this
document, we therefore explain this phenomenon, by showing the effect of
indirect dependencies on the application of the MI approach to the mixing and
separating models considered in [4]. We thus introduce a corrected expression
of the gradient of the considered BSS criterion based on MI. This correct
gradient may then e.g. be used to optimize the adaptive coefficients of the
considered separating system by means of the well-known gradient descent
algorithm. As explained hereafter, this investigation has some similarities
with an analysis that we previously reported in another arXiv document [3].
However, these two investigations concern different problems (mixture and
separating structure, mathematical tools: see paper).
