I have an Android phone, but what is described in the post sounds a lot like what the app Average Cam Pro [1] does on my iPad (multiple exposures, average them out) with the refinement that the ACP app also allows you to subtract a "dark image" to combat sensor-specific banding noise, plus the user can adjust exposure after the shot.
It takes the cleanest pictures by far, beating out my Canon 7D at times, but for optimal results it does require the device to be extremely steady. I've been waiting for this app to appear on Android too, but it hasn't so far.
Edit: I just discovered Flickr is filled with em. Some good examples on what happens when the number of shots you select (anywhere from 4-64 I believe) is less than optimal if you scroll down:
https://www.flickr.com/search/?q=%23avgcampro
I use Avg Cam Pro in touristy situations with lots of movement. Take 64 shots and (moving) people simply fade away by the time you're done.
It takes the cleanest pictures by far, beating out my Canon 7D at times, but for optimal results it does require the device to be extremely steady. I've been waiting for this app to appear on Android too, but it hasn't so far.
[1] https://itunes.apple.com/us/app/average-camera-pro/id4155778...