The first thing to try would be the various "paint free" automotive dent removal techniques like suction cups. Some forums members have had good luck hot-gluing a large nail head to the dent and then giving a yank on the nail shaft. A dent like this isn't just going to "pop" out and be unnoticeable, but you may be able to get it pulled out with only minimal rippling and crinkling visible (the metal actually stretches from this kind of dent).
If you want to really get into it, you could remove the interior walls and try to "roll" the dent out from behind. Rolling dents is more art then skill, and it is possible to make an even worse mess of the dent (believe me, I have).
The only way to restore it to brand new appearance would be to replace the segments. You can do this yourself as well, but it is no simple task. The panels themselves, with shipping will run you about $500 apiece.
Last I heard, professional segment replacement usually runs about $2000 per segment, and you have two dented segments. Why not use insurance?