On the slab area, you'd either need to do it with electric heating mats and probably tile (lowest buildup), or lots of cuts to bury pex in it, or pour a lot of additional cement over it, or use something like Bekotec from http://www.schluter.com/9_1_schluter_bekotec.aspx, then tile it. On a wooden subfloor, you can staple up plates and add pex. There are probably a few other ways, as well, but that's what comes to mind. Without chopping up the slab, I think the Schluter product may end up with the least buildup if you go hydronic on the slab. There are some ply/metal track systems, but I do not know if they are acceptable for use on a slab...I know they are designed for subfloors. Anchoring them in the slab is going to be a bit of a pain, but not too bad with the right tools (either shoot fasteners or a hammer drill and use screw anchors).
If the slab does not have a moisture barrier and insulation underneath, you need to be much more careful of your selection - heating up the ground underneath can get expensive!