Algorithm for separating signals

Algorithm for separating signals

I have a image (I) and a background image (B). I would like to find an
algorithm for separating the foreground.
At the moment I am using fourier transforms to do this with some success.
invF(F(I) - F(B))
Where invF is the inverse fourier transform.
This works pretty well in cases the forground of the image is transparent.
However in situations where the fourground is not transparent, I use
invF(F(I) - a.F(B))
where a is a small constant ~ 0.1
It would be good to have a formal way of choosing 'a' to get the best results