Apps purchased on iPhone not showing up in iTunes

I've bought a fair number of apps through the App Store, including some reasonably expensive ones. I've also had severe problems backing up my iPhone, and eventually had to restore it from scratch so that I could update with the latest OS. Unfortunately, none of the apps which I bought on the App Store have shown up in iTunes, and thus I can't reload them. How do I go about restoring these apps without buying them?