Question

Hello.
This problem is about image noise cancelling. The problem is like this:

There are some pictures of moon that you take in a row. The position of moon doesn't change at all and there exists white Gaussian noise on the image. Mean of the noise is 1 and variance is 49. How do you get a clean image without noise?

There is a comment for this problem that if you average k pictures which satisfy the condition ?^2 / k < 1, which is same as 49 / k < 1 in this case, then you can get a clean image. How can I solve this problem? I have no idea whether this is true or not. What I know about the variance of Gaussian distribution is just that it is same as E[(X-m)^2] = E[X^2] - E[X]^2. Thank you for your help.

Answer 1

All you need to find is how many images that you need to consider to get an image without noise.

Here the standard error for the mean noise is as you stated in the question.Reducing the standard error would increase the possibility of getting a clean image without noise. ie by making the square of the standard error less than the mean value or in otherwords If 49/k<1 then a clean image is obtained.

which implies k>49. So if you take 50 or more images then you get a clean image without noise.