# MSE Mean Square Error

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Soum on 3 Jul 2013
Edited: DGM on 12 Feb 2023
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

Image Analyst on 3 Jul 2013
See my demo:
% Demo to calculate PSNR of a gray scale image.
% http://en.wikipedia.org/wiki/PSNR
% 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.
[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);
message = sprintf('The mean square error is %.2f.\nThe PSNR = %.2f', mse, PSNR);
msgbox(message);
DGM on 12 Feb 2023
Edited: DGM on 12 Feb 2023
From the imnoise() synopsis:
J = imnoise(I,'salt & pepper',D) adds "salt and pepper" noise to the
image I, where D is the noise density. This affects approximately
D*numel(I) pixels. The default for D is 0.05.
So D can obviously be anything from 0 to 1. Values outside that range will result in an error message.
Also from the synopsis:
The mean and variance parameters for 'gaussian', 'localvar', and
'speckle' noise types are always specified as if for a double image
in the range [0, 1].
So M can be anything real, and V can be anything real and positive. Given the fact that we're working in unit-scale though, it wouldn't make sense for V to be very large or for the magnitude of M to be far from zero.

ashkan abbasi on 11 Apr 2014
% MSE & PSNR for a grayscale image (cameraman.tif) & its filtered
% version
clear
clc
im=im2double(im);
h1=1/9*ones(3,3);
imf1=imfilter(im,h1,'replicate');
h2=1/25*ones(5,5);
imf2=imfilter(im,h2,'replicate');
%
MSE1=mean(mean((im-imf1).^2));
MSE2=mean(mean((im-imf2).^2));
MaxI=1;% the maximum possible pixel value of the images.
PSNR1=10*log10((MaxI^2)/MSE1);
PSNR2=10*log10((MaxI^2)/MSE2);
Rasheed Khankan on 14 Mar 2016
Great, concise, and operative code... Thanks a lot.

Desmond Michael on 10 Feb 2016
Edited: Rik on 2 Feb 2022
Hello everyone, I've found a website regarding the above and its very helpful. http://vaaiibhav.me/calculating-the-psnr-and-mse-code-matlab/
Edit @Rik:
The link seems to have gone down. Here is a capture of that page from 2019.
DGM on 12 Feb 2023
Note that if you have a version newer than R2014x and you don't have psnr() or immse(), bear in mind that both are still part of the Image Processing Toolbox, so you'll also need that.

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