Denote one of the source signals in the optimal solution as . By optimality we mean that the standard EM-algorithm will eventually converge to with . When we have not yet found the optimal vector , we have where . G is mostly due to the other sources and to a small extent the Gaussian noise in the data. We can think that the E-step filters away the noise by making use of the knowledge about the prior distribution of s .
G is due to other sources and a slow convergence results.
From this point of view, it is obvious that we can speed up the convergence if we can filter away also that part of s G which is due to other sources. When we are far from the optimal solution, it is natural to assume that and . Since a and s 0 are linearly related, we get If we can compute a G , we can adjust the vector a to take into account the apparent noise due to other sources. By the central limit theorem, the distribution of the sum of contributions from several other sources approaches Gaussian as the number of other sources increases. The Gaussian source s 0 G is the projection of Gaussian noise to the subspace spanned by a and therefore represents the contribution of the other sources and some Gaussian noise to the estimated source s 0 .