Separating independent sources from available signals.

I have four signals in time domain, in the format of 4 vectors (a,b,c,d). I know there are 3 sources contributing these signals.

One is a source that is shared between all four signals.

One is a source that is shared between only two of them, for instance between a and b.

The last one is a source that is shared between the other two, for instance between c and d.

I want to know whether it is mathematically possible to extract these three sources from my signals and how.

In addition, if each signal is contaminated by independent noise source (most likely gaussian noise), how does it affect my solution?

Thanks.