Capturing a full-res photo while recording a video?

I know many phones now have the ability to capture photos while recording photos but all the phones I know that have this feature only takes photos with the resolution of the video and is not taking advantage of the full resolution of the camera. Do you know a phone that has the feature that I want or is it not possible to do this on a mobile phone?

Btw, if you know a camera (not necessarily a phone) that does this, please include it.