MATLAB Answers


MSE Mean Square Error

Asked by Soum
on 3 Jul 2013
Latest activity Commented on by Image Analyst
on 30 Dec 2018 at 15:21
I De-noise some images and I want to evaluate them so I calculate SNR but I want to use another like Mean Square Error (MSE) I saw some people use it but I don't know what is express in my case I have a noisy image like input and De-noised one in the out put Or maybe PSNR please help me

  1 Comment

I want to calculate the mean square error of the desired(ideal) QMF filter and the designed QMF filter using matlab in order to optimize the filter using ABC and PSO algorithms.Can someone help me with the code please???

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5 Answers

Answer by Image Analyst
on 3 Jul 2013
 Accepted Answer

See my demo:
% Demo to calculate PSNR of a gray scale image.
% Clean up.
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;
%------ GET DEMO IMAGES ----------------------------------------------------------
% Read in a standard MATLAB gray scale demo image.
grayImage = imread('cameraman.tif');
[rows columns] = size(grayImage);
% Display the first image.
subplot(2, 2, 1);
imshow(grayImage, []);
title('Original Gray Scale Image', 'FontSize', fontSize);
set(gcf, 'Position', get(0,'Screensize')); % Maximize figure.
% Get a second image by adding noise to the first image.
noisyImage = imnoise(grayImage, 'gaussian', 0, 0.003);
% Display the second image.
subplot(2, 2, 2);
imshow(noisyImage, []);
title('Noisy Image', 'FontSize', fontSize);
%------ PSNR CALCULATION ----------------------------------------------------------
% Now we have our two images and we can calculate the PSNR.
% First, calculate the "square error" image.
% Make sure they're cast to floating point so that we can get negative differences.
% Otherwise two uint8's that should subtract to give a negative number
% would get clipped to zero and not be negative.
squaredErrorImage = (double(grayImage) - double(noisyImage)) .^ 2;
% Display the squared error image.
subplot(2, 2, 3);
imshow(squaredErrorImage, []);
title('Squared Error Image', 'FontSize', fontSize);
% Sum the Squared Image and divide by the number of elements
% to get the Mean Squared Error. It will be a scalar (a single number).
mse = sum(sum(squaredErrorImage)) / (rows * columns);
% Calculate PSNR (Peak Signal to Noise Ratio) from the MSE according to the formula.
PSNR = 10 * log10( 256^2 / mse);
% Alert user of the answer.
message = sprintf('The mean square error is %.2f.\nThe PSNR = %.2f', mse, PSNR);


Somehow your cameraman.tif must have turned into a color image. The version of it that ships with MATLAB is definitely a grayscale image. What does this say:
[rows, columns, numberOfColorChannels] = size(grayImage)
It should say 256, 256, 1. If the third number is 3 then either you changed my demo to use a color image (most likely) or else somehow your cameraman.tif image is not the original one.
I think that the maximum value is 255 not 256.
on 2 Oct 2017
That may well be. But he's referring to the dimensions of the image, not the pixel value.

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Answer by ashkan abbasi on 11 Apr 2014

% MSE & PSNR for a grayscale image (cameraman.tif) & its filtered
% version
MaxI=1;% the maximum possible pixel value of the images.


Great, concise, and operative code... Thanks a lot.
no ur
on 30 Dec 2018 at 14:12
PSNR and MSE according to bitrate????
Image Analyst
on 30 Dec 2018 at 15:21
no - I have no idea what you're intending. Is this a question, or are you're just surprised at something unexpected that was said? Please ask a fully grammatically complete question if you have one. Otherwise I'm not sure people will respond to you in a way that is useful to you and give you exactly what you want.

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Answer by jensi asir on 18 Jan 2014

im also getting the same message which show 3 times psnr values ? whats the wrong in it.can you please help me

  1 Comment

You probably changed my demo to use a color image of your own.

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Answer by iza
on 20 Jan 2015

Can anyone check mine? Is it correct?...
%Load single MRI image I = imread('IM_00042.tif');
% addition of graininess (i.e. noise) I_noise = imnoise(I, 'gaussian', 0.09);
% the average of 3^2, or 9 values(filters the multidimensional array A with the multidimensional filter h) h = ones(3,3) / 3^2; I2 = imfilter(I_noise,h);
% Measure signal-to-noise ratio img=I; img=double(img(:)); ima=max(img(:)); imi=min(img(:)); mse=std(img(:)); snr=20*log10((ima-imi)./mse)
% Measure Peak SNR [peaksnr, snr] = psnr(I_noise, I); fprintf('\n The Peak-SNR value is %0.4f', peaksnr); fprintf('\n The SNR value is %0.4f \n', snr); fprintf('\n The MSE value is %0.4f \n', mse);
%Plot original & filtered figure
subplot(1,2,1), imshow(I_noise), title('Original image')
subplot(1,2,2), imshow(I2), title('Filtered image')
text(size(I,2),size(I,1)+15, ...
'Gaussian = 0.09', ...


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Answer by Desmond Michael on 10 Feb 2016

Hello everyone, I've found a website regarding the above and its very helpful.


I don't see anything there at that web site - no zip file or download link like it says. Anyway, since my answer above, MATLAB has added built-in functions immse() and psnr() to make it easy for you.
Why is my Matlab is displaying
immse not found
and also psnr() is not there. Which versions support these built in functions?
immse() was introduced in R2014b and psnr() was introduced in R2014a. See my attached demo where I do it without toolbox functions, and as given in my Answer way up at the top.

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