# ICA - extract one non-Gaussian source among many Gaussian sources with a-priori information

I have $N$ mixtures consisting of one non-Gaussian source (I know the distribution) and many (more than $N$) Gaussian sources.

I also know how my non-Gaussian source is mixed into the signal (I know the elements of A that relate my non-Gaussian source to the mixture in $x=As$).

I have no information about my Gaussian sources, except for the fact that they are Gaussian and separated in space. My Gaussian sources have an unknown mean that is not zero.

Is there a way I can reconstruct my non-Gaussian source? I tried it with one Gaussian source and it works. But as soon as I activate multiple Gaussian sources it degrades my reconstruction too much.

Any literature hints would be appreciated!