RomanM has just completed a short post describing the reasons and a few methods behind RegEM on his blog Statpad.
Imputation, EM and RegEM
This is not intended to be an in-depth mathematical treatment of the subject although some prior linear algebra and matrix methodology is needed to understand some of theconcepts. Rather, it is more a statement of the underlying problem, some of the assumptions involved and an intuitive view of how the methods work. Some prior understanding of multivariate statistical structures and how relationships are measured is also assumed, but I will try to keep it as short and simple as possible.
If you’re interested in RegEM it’s worth your time.