Image averaging for impulse noise

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Hello,

Why does image averaging ( taking the average of many images ) not work for impulse noise ? I understand the mathematics of why it works for gaussian noise. Since we can treat the noisy image as an addition of the original image with the noise, image averaging reduces the variance.

But why can't it work for impulse noise ? Would it be because there is no mathematical way of showing the addition of impulse noise to the original image ?