Picture with rear camera causes complete power off and lock

I've got a strange intermittent fault with an iPhone 4 16gb. Sometimes, but not always, taking a picture with the rear camera causes the phone to go completely dead, even on a full charge. I can restart the phone only by holding both the font and top buttons until the Apple logo appears. Often when this happens the phone will only stay on for a 30 seconds or so before it powers off again. The only resolution is then to restart when connected to a power source when the phone will show the fact that the battery has quite a charge in it.

The fault sounds like a battery related issue to me, but the randomness of it related to the camera baffles me.

Anyone experienced this before and would a battery swap fix this or could it be a power short on the camera circuitry?

Thanks.