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

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.

Answer 1

[Image Analyst]

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.

[Mohsin Shah]

I know about imnoise and randn but my question is about standard deviation of 64 gray levels. I mean what is the relationship between standard deviation and gray levels when we say standard deviation of 64 gray levels.

[Image Analyst]

It means that your gray levels change value such that the square root of the sum of the squares of the actual gray levels minus the mean of the gray levels is 64. Just the standard formula for standard deviation. Go here Wikipedia Standard Deviation if you don't know "what is the relationship between standard deviation and gray levels". It's just the standard formula everyone uses.

I guess I'm not sure what you're confused about. If you know you want it, then I would think you should already know what it is, what it means, and how to compute it.

[Mohsin Shah]

Thank you Image Analyst.

[Image Analyst]

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.
noiseAddedImage = double(grayImage) + noiseOnlyImage;
% Compute the standard deviation of the three images.
sdGray = std(double(grayImage(:)))
sdNoiseOnly = std(noiseOnlyImage(:))
sdNoiseAdded = std(noiseAddedImage(:))
% Compute the means of the three images.
meanGray = mean(double(grayImage(:)))
meanNoiseOnly = mean(noiseOnlyImage(:))
meanNoiseAdded = mean(noiseAddedImage(:))

%======================================================
% 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);
imshow(noiseAddedImage, []);
title('Noise-Added Image', 'FontSize', 20);
% Display its histogram
subplot(2, 3, 6);
histogram(noiseAddedImage, 'EdgeColor', 'none');
grid on;
caption = sprintf('Histogram of Noise-Added Image\nMean = %.2f, SD = %.2f', meanNoiseAdded, sdNoiseAdded);
title(caption, 'FontSize', 20);

[Mohsin Shah]

Thank you so much, your answers are always fascinating and I learn more than I expect. I got my answer.

Answer 2

[lakpa tamang]

why is the mean not 0 in your code, yet he is asking for awgn?

[Image Analyst]

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.