How can I perform object tracking using noisy images? The problem

Take 50+ of Lena images, add gaussian noise to them to the point that you couldn't say it is Lena. I insist, gaussian noise, not gaussian blurring.

Now imagine a cropping window randomly moving around Lena's face (like a video camera focused on this part).  

Now you have a handful of noisy pictures containing what used to be Lena's face somewhere in the image.  

The question

Now I want to get back the face without knowing it in advance :)


First I have to identify overlapping parts (i.e. noisy faces here) from the set of images.
Then I must superimpose the faces.
And finally, add them to get back her beautiful face.


The problem is that I have no clue of how to do that (cross correlation, perhaps to identify the faces and the shift between them).
I've never had courses in image processing. I just need a reference or an algorithm name.
If the noise levels added to each pixel are independent, perhaps blurring the images first and then applying a pairwise cross-correlation could do the job.