noise reduction

Question

I have an image with uniform intensity everywhere with gray value = 100 then i added additive zero-mean independent Gaussian noise with standard deviation = 5

I = ones(100,100)*100;
I_n=I+(5*randn(100,100));

I think that the mean and standard deviation of the pixel intensity in the noisy image will be 100 and 5 respectively,

then i want to reduce the noise in the noisy image by 2x2 averaging mask.

what is the effect of the averaging mask on the mean and standard deviation of the pixel intensity in the image? is it better to increase the size of the mask?

Answer 1

for a uniform original image, and uniform noise, averaging won't change the mean. it will reduce the variation between pixels, but also make the noise between adjacent pixels correlated.

if you calculated the standard deviation then you would find that the value is 2.5 (reduced by a factor of 2, 2 = sqrt(4), where you averaged 4 values).

using a larger mask will reduce the noise further, but correlate it over more pixels. it will also blur more any structure in the underlying image (not an issue in this case, because it is uniform).

Answer 2

Standard averaging techniques will not work well in these situations. Just use a Wiener Filter if you have the autocorrelation matrices, else use Gaussian Process Regression with a suitable kernel matrix.