If you only need to remove the noise by averaging, you can layer the images in photoshop with transparency (Bottom layer 100%, next layer 50%, 3rd layer 25%, 4th layer 12%, and so on).
Are you sure it shouldn't be 100%, 50%, 33%, 25%, 20% and so on?
Suppose you have 4 images: A,B,C,D
Your numbers give:
layer1: 100% A
Adding layer2: 50% layer2 + 50% lower layers = 50% B + 50% A
Adding layer3: 25% layer3 + 75% lower layers = 25% C + 75% * (50% B + 50% A)
= 25% C + 37.5% B + 37.5% A
Adding layer4: 12% layer4 + 88% lower layers = 12% D + 88% (25% C + 37.5% B + 37.5% A)
= 12% D + 22% C + 33% B + 33% A
My numbers give:
layer1: 100% A
Adding layer2: 50% layer2 + 50% lower layers = 50% B + 50% A
Adding layer3: 33% layer3 + 67% lower layers = 33% C + 67% * (50% B + 50% A)
= 33% C + 33.5% B + 33.5% A
Adding layer4: 25% layer4 + 75% lower layers = 25% D + 75% (33% C + 33.5% B + 33.5% A)
= 25% D + 24.75% C + 25.125% B + 25.125% A
Anyway, I once tried the same with some extremely zoomed-in pictures of Jupiter to see if I can find the Jovian moons. I failed, and I figured out later why: to increase my
SNR sufficiently, I'd need hundreds of images.
The problem is that the noise only goes down with the square root of the number of images. So, to give you an idea:
Code:
# images Noise (percentage of noise in single image)
1 100%
2 71%
3 58%
4 50%
10 32%
100 10%
You'll not be able to get rid of light pollution by these methods, as the light pollution is an inherent part of the scene that you took the photos of. There are ways to get rid of light pollution. It basically requires taking a copy of the image as a new layer and applying a large gaussian blur to it (that essentially blurs out all stars. Since the light polliution is diffuse anyway, the blur doesn't really affect it so you end up with an image that is pretty much just the light pollution). You can then subtract this blurred image from the original which essentially gets rid of the light pollution. Google some words for better information and, I'm sure, lots of blogs on the subject.
That sounds like a nice method. Basically, it leaves you with all sharp objects, so it's a kind of sharpening filter (the imaging equivalent of a high-pass filter). Unfortunately, noise is also quite sharp, so it gets rid of the overall background light, but you don't get rid of the 'grass'.