I think it may be a double weave (which basically means to weave two layers of fabric at once) which is joined together at the curvy diamond shapes (the lighter threads at the back layer brought forward to make the pattern) the flowers (the warp of the back layer pulled forward and held around a dowel to form loops) and the knots. (I'm calling them knots for lack of a better term but I think they are actually more loops which have been woven in again after several rows.)
I think I could get the loops at the edges just by leaving some extra thread at the edge at each pass--possibly held by another dowel for consistency of size and tension.
Mind you, I haven't actually woven a thing since high school, and even then it was never this complicated, but I think the theory is sound and worth trying. I guess my next step would be to investigate looms...
