Centering

The most basic and necessary preprocessing is to center ${\bf x}$, i.e. subtract its mean vector ${\bf m}= E\{{\bf x}\}$ so as to make ${\bf x}$ a zero-mean variable. This implies that ${\bf s}$ is zero-mean as well, as can be seen by taking expectations on both sides of Eq. (4).

This preprocessing is made solely to simplify the ICA algorithms: It does not mean that the mean could not be estimated. After estimating the mixing matrix ${\bf A}$ with centered data, we can complete the estimation by adding the mean vector of ${\bf s}$ back to the centered estimates of ${\bf s}$. The mean vector of ${\bf s}$ is given by ${\bf A}^{-1} {\bf m}$, where ${\bf m}$ is the mean that was subtracted in the preprocessing.