I don't know if this will work but try cycling back and forth between invert colours and normal colours a few times. A post I found online mentioned that it worked. If it doesn't work and resetting all settings doesn't work, you may want to have it checked out at the Genius Bar at the nearest Apple Store to see if a full diagnostic can track down the problem.
Edit: Marilyn's excellent post has what I believe to be the right answer.
Could you have accidentally turned on the grayscale feature [that came with iOS 8]?
To see if it's on, go to Settings > General > Accessibility and look for the line titled "Grayscale." If it's on, the button will be to the right. To turn it off, tap the button or slide it to the left.