It seems like others have had this problem as well:
http://www.reddit.com/r/GalaxyNexus/comments/19y0a9/galaxy_nexus_screen_turn_on_durring_lock_screen/
http://productforums.google.com/forum/#!topic/mobile/PA5JZH-Oj4o
http://code.google.com/p/android/issues/detail?id=39625
It is a bug in Android 4.2, specifically with the Samsung Galaxy Nexus. I imagine you recently updated your phone, which is why it has only been occurring as of late.
It looks like the cause is from app notifications being pushed to the device and waking it up. Here are some common apps that have been known to cause this problem:
WeChat
Sleep Mode apps
MX Player
DropSync
Disabling auto-sync has also been known to solve this problem:
Thesettings> data usage> and disable auto sync and restrict background data
Some people have also had success just doing a factory reset.
A lot of people have had a lot of success getting rid of this problem by reverting back to 4.1.2.
Others have followed this approach and had a lot of success:
I had this same problem and I tried disabling apps, uninstalling apps, and factory resetting all with no success. What fixed it for me was taking a very small flat-head screwdriver and gently bending the pins of the micro USB connector up (towards the screen side).
Over time and through usage, those pins got bent downward, away from the screen side. I think this created some kind of electrical short. I tried this because when the phone was plugged in, the screen stayed asleep.
My GNex is now working perfectly again. I hope this helps someone!
HOW TO FIX PROBLEM
The problem is that the hooks inside your charging port are too close to the bottom. Therefore with a small knife or needle, life the middle part up nearer to the screen and Voila! Your problem should be fixed. Its not the software. Its the hardware .
This seems to be a very weird problem with a lot of different causes. Some people have had success with removing or modifying the software, other people think that it's the pin problem. If you get any of these solutions to work, let me know. Hope this helps!
John