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 2018-7-12

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评论： Image Analyst 2019-12-13

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.

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Answer 1

Image Analyst 2018-7-12

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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.

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Image Analyst 2018-7-13

编辑：Image Analyst 2019-12-13

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 2018-7-13

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

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Answer 2

lakpa tamang 2019-12-13

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

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Image Analyst 2019-12-13

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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