i need matrix n which generated

snr=mean2(I./n)=0.5 ;where I is original image matrix and n is a noise matrix of same size of I.

if i have 'I',i need matrix n which generated using n=mm+sqrt(vv)*randn(size(I)) such i can get snr=0.5.

[José-Luis]

What have you tried so far?

[Image Analyst]

Lots of things (click on his name), but he has never asked the right questions until now. He may have it right now, but I'm not sure.

Answer 1

[Image Analyst]

If n = 2*I, on average, then the SNR will be 1/2. So what do you get if you scale n so that the mean of n equals twice the mean of I? Give that a shot.

[Edit/addition]

Haven't heard from you so I guess you're having trouble. Here, run this code for a demo:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables.
workspace;  % Make sure the workspace panel is showing.
format longg;
format compact;
fontSize = 20;

% Read in a standard MATLAB gray scale demo image.
folder = fullfile(matlabroot, '\toolbox\images\imdemos');
baseFileName = 'cameraman.tif';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
if ~exist(fullFileName, 'file')
  % File doesn't exist -- didn't find it there.  Check the search path for it.
  fullFileName = baseFileName; % No path this time.
  if ~exist(fullFileName, 'file')
    % Still didn't find it.  Alert user.
    errorMessage = sprintf('Error: %s does not exist in the search path folders.', fullFileName);
    uiwait(warndlg(errorMessage));
    return;
  end
end
grayImage = imread(fullFileName);
% Get the dimensions of the image.  
% numberOfColorBands should be = 1.
[rows columns numberOfColorBands] = size(grayImage);
% Display the original gray scale image.
subplot(2, 3, 1);
imshow(grayImage, []);
title('Original Grayscale Image', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Give a name to the title bar.
set(gcf,'name','Demo by ImageAnalyst','numbertitle','off') 
colorbar;

% Get the mean of the image
meanGL = mean2(grayImage)

% Specify the variance, it can be anything at all.  It doesn't matter.
% Ask user for a number.
defaultValue = 50;
titleBar = 'Enter a value';
userPrompt = 'Enter the standard deviation (it will not affect the SNR)';
caUserInput = inputdlg(userPrompt, titleBar, 1, {num2str(defaultValue)});
if isempty(caUserInput),return,end; % Bail out if they clicked Cancel.
desiredStandardDeviation = str2num(cell2mat(caUserInput));
% Check for a valid number.
if isnan(desiredStandardDeviation)
    % They didn't enter a number.  
    % They clicked Cancel, or entered a character, symbols, or something else not allowed.
    desiredStandardDeviation = defaultValue;
    message = sprintf('I said it had to be an integer.\nI will use %d and continue.', desiredStandardDeviation);
    uiwait(warndlg(message));
end
desiredvariance = desiredStandardDeviation ^2; 
% Create the noise image using his formula:
noiseImage = 2 * meanGL  + sqrt(desiredvariance)*randn(size(grayImage));
% Don't allow noise to be negative
noiseImage = max(noiseImage, 0);
% Display the image.
subplot(2, 3, 2);
imshow(noiseImage, []);
colorbar;
title('Noise Image', 'FontSize', fontSize);

% Calculate the SNR
SNR = mean2(double(grayImage) ./ noiseImage)

% Add them together
noisyImage = double(grayImage) + noiseImage;
% Display the image.
subplot(2, 3, 3);
imshow(noisyImage, []);
colorbar;
caption = sprintf('Noise Image with SNR = %.4f', SNR);
title(caption, 'FontSize', fontSize);

message = sprintf('The SNR for these images is %.4f', SNR);
uiwait(helpdlg(message));

% Because it's random, you can't make it exactly 0.5 until you know what it actually is.
noiseImage2 = noiseImage * SNR / 0.5;
% Display the image.
subplot(2, 3, 5);
imshow(noiseImage2, []);
colorbar;
title('Noise Image', 'FontSize', fontSize);
% Add them together
noisyImage2 = double(grayImage) + noiseImage2;
% Now it should be 0.5
% Calculate the SNR
SNR2 = mean2(double(grayImage) ./ noiseImage2)
% Display the image.
subplot(2, 3, 6);
imshow(noisyImage2, []);
colorbar;
caption = sprintf('Noise Image with SNR = %.4f', SNR2);
title(caption, 'FontSize', fontSize);
message = sprintf('The SNR for these images is %.4f', SNR2);
helpdlg(message);

[vipul utsav]

if i want snr=0.9 then how can i generated n using

mean+sqrt(variance)*randn(size(grayImage));?

because in your above code if i change variance in

noiseImage = 2 * meanGL + sqrt(desiredvariance)*randn(size(grayImage)); then

snr remains 0.5 same.(not depends on variance),but noise is depends on variance,

so i need noise matrix 'n' such that i can get my desired snr value('n' is depends on variance and it is generated using mean+sqrt(variance)*randn(size(grayImage)))

[Image Analyst]

You need to study to code so you understand it. See the line:

noiseImage2 = noiseImage * SNR / 0.5;

? That 0.5 was your your desired SNR. Change it to whatever you want.

[vipul utsav]

   noiseImage2 = noiseImage * SNR / 0.8;

i have studied your whole code,,then i got noiseImage2 using above line that gives me 0.8 SNR. it is ok

But,this is a fix matrix which gives 0.8 SNR, if i find variance of noiseImage2 and then i generate noiseImage of variance equal to noiseImage2(1086.72) using

   noiseImage = 2 * meanGL + sqrt(desiredvariance)*randn(size(grayImage))

then it gives me a 0.5 SNR,but i want 0.8 SNR,

i hope you understand my comment and you would give me right solution

[Image Analyst]

Regarding your "Answer" below (which is not really an Answer, is it, it's really a comment to my Answer)...

You still do not understand the formulas. See that 2? Recall that that 2 came from you wanting an SNR of 1/2. So it should be 1/0.8. Here's what the lines should be to be more general.

% Create the noise image using his formula:
desiredSNR = 0.8;
noiseImage =  meanGL/desiredSNR  + sqrt(desiredvariance)*randn(size(grayImage));
% Don't allow noise to be negative
noiseImage = max(noiseImage, 0.01);

and then later on down in the code:

noiseImage2 = noiseImage * SNR / desiredSNR;

This is what happens when you give a very very specific case and don't let us know in the beginning what factors are supposed to be variable/general. In the future, let us know what factors are to be held constant and what factors might you want to vary. Thanks.

[vipul utsav]

if any element in noiseImage is '0' then SNR becomes infinite, so can i neglect this pixel?

and if i neglect it,it definitely effect on mean and variance of noiseImage but how much amount it effects on variance of noiseImage?

[Image Analyst]

I had that case and I got inf, so you can see that I changed the min allowable value to 0.01. Doing that didn't affect the SNR much as compared to ignoring that pixel totally because there were so few pixels it affected.

[Image Analyst]

You might try checking out this File Exchange submission: http://www.mathworks.com/matlabcentral/fileexchange/25645