Effect of σ on Gaussian noise

noise = randn(size(im)).*sigma;
Sigma = 2, 8, 32, 64

noise = randn(size(img)).* 2;
output = im + noise;

First attempt at a solution
Replace each pixel with an average of all the values in its neighborhood – a moving average;
original -> smoothed

Average assumptions
1. the true value of pixels are similar to the true value of pixels nearby.
2. the noise added to each pixel is done independently.