This is derived from practically all the answers above. Please credit them with 99% of any credit this gets.
From all the various answers and from current knowledge of brain anatomy, it seems that the two halves of the brain are not identical, and they fulfill different functions. Direct communication between the two halves of the brain seem necessary to the regeneration process, and that is not enough. The head must be connected to the body (sew it back together?). Can we call it regeneration then? It seems more like resurrection or reanimation.