Removing 'Black Sun' From Video

I am capturing video from a cheap, light-weight camera that turns the sun black (presumably to protect the sensor in the camera). When it appears, this black disc in the sky -- usually surrounded by a blazing white halo -- looks weird, and I'd like to remove it.

Does anyone have a similar problem? Can anyone suggest a simple mechanism for white-ing out or otherwise eliminating this black sun?

Thanks...