This may help some people.
1. Go to iTunes on your computer. Go up to the top where it says "FIle Edit View, etc." and click on "View" Then go down to "Sidebar" and make sure "Show Sidebar" has been clicked.
2. Now go to the Sidebar, and under library, see if "Apps" is present. If not, go up to the top, and click on "iTunes", then "Preferences" then, click under "General" make sure "Apps" has a check mark by it.
3. Then go to the Sidebar, and click on "Apps" and see if any Apps are present. If not, then this is a problem.
4. In the Sidebar, click on "iTunes Store", then, on the right hand side of "iTunes Store", under "Quick Links" click on "Purchased."
5. Then, at the top of this page, under "Purchased", click on "Apps." See if any Apps show up. If they have a little "cloud" in the upper right corner, then they haven't been downloaded to this particular computer.
6. Go to the bottom of this page, and click on "Download All". All of your purchased apps should begin to download onto this particular computer.
7. Then, wait to download all of your Apps. This could take a while.
8. Then, restore your iPhone from backup, and the Apps should appear.
I hope this helps someone. If this helps you, post a response so that others will know whether it works.
Good luck.