# How to add to an image white Gaussian noise of zero mean and standard deviation of certain gray levels?

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Mohsin Shah on 12 Jul 2018
Commented: Image Analyst on 13 Dec 2019
Hello everyone, How can we add white Gaussian noise to an image with zero mean and standard deviation of 64 gray levels? I do know how to add noise of zero mean and variance using imnoise but I do not know about standard deviation of 64 gray levels.

Image Analyst on 12 Jul 2018
Did you try imnoise() or randn()? If not, why not? They're so easy that you should be able to figure them out on your own.
Image Analyst on 13 Jul 2018
Edited: Image Analyst on 13 Dec 2019
OK, I sense that you tried but couldn't do it, so here is a full demo:
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
clear; % Erase all existing variables. Or clearvars if you want.
workspace; % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
% Make a gray scale image of brightness 128 gray levels.
grayImage = 128 * ones(480, 640, 'uint8');
% Make a noise image of standard deviation 64 gray levels.
noiseOnlyImage = 64 * randn(480, 640);
% Add the noise image to the gray scale image.
% Compute the standard deviation of the three images.
sdGray = std(double(grayImage(:)))
sdNoiseOnly = std(noiseOnlyImage(:))
% Compute the means of the three images.
meanGray = mean(double(grayImage(:)))
meanNoiseOnly = mean(noiseOnlyImage(:))
%======================================================
% Now plot everything.
subplot(2, 3, 1);
imshow(grayImage);
title('Original Image', 'FontSize', 20);
% Display its histogram
subplot(2, 3, 4);
imhist(grayImage);
grid on;
caption = sprintf('Histogram of Original Image\nMean = %.2f, SD = %.2f', meanGray, sdGray);
title(caption, 'FontSize', 20);
subplot(2, 3, 2);
imshow(noiseOnlyImage, []);
title('Noise-Only Image', 'FontSize', 20);
% Display its histogram
subplot(2, 3, 5);
histogram(noiseOnlyImage, 'EdgeColor', 'none');
grid on;
caption = sprintf('Histogram of Original Image\nMean = %.2f, SD = %.2f', meanNoiseOnly, sdNoiseOnly);
title(caption, 'FontSize', 20);
subplot(2, 3, 3);
% Display its histogram
subplot(2, 3, 6);
grid on;
title(caption, 'FontSize', 20);
Mohsin Shah on 13 Jul 2018

lakpa tamang on 13 Dec 2019
why is the mean not 0 in your code, yet he is asking for awgn?
Image Analyst on 13 Dec 2019
I used randn() to get 640*480 = 307,200 samples. Since these are RANDOM, the mean will not necessarily be exactly at zero. Imagine if you asked for only 4 values. Would you expect the value to be at exactly zero:
>> r=randn(1, 4)
r =
-0.740261712090743 -0.384816596337627 -0.581927647800475 1.27720101511378
>> mean(r)
ans =
-0.107451235278765
See, not exactly zero even though randn() draws from a standard normal distribution.
I don't know how important it was to him to have a mean of exactly zero versus having random numbers drawn from a distribution. I'd imagine having the random numbers is fine and the fact that they don't have a mean of exactly zero doesn't really matter to him. If it did, he could subtract the mean or something like that.

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