1. A blur correction camera system comprising: a vibration detection unit that detects a vibration and outputs a vibration detection signal; a blur correction optical system that is driven based upon the vibration detection signal and corrects an image blur; an image-capturing unit that captures an image formed with a photographic optical system that includes the blur correction optical system; and an image restoration computing unit that corrects an image blur by executing image restoration through image processing on an image captured by the image-capturing unit.