frequency domain filter problem ??

The image houseNoisy.gif is corrupted with periodic additive noise. Design the appropriate filter in the frequency domain that is capable of attenuating the noise in the image ,, so my image already has an additive noise ,, can u provide me a code to do this thing ! this is the image : http://tinypic.com/r/2vvvxu8/5

Answer 1

[Image Analyst]

Here's a demo. You can adapt it to solve your homework problem.

% Demo to filter an image, with periodic ripple, in the Fourier domain.
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 = 14;

% 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);
[rows columns numberOfColorBands] = size(grayImage);
if numberOfColorBands > 1
  grayImage = rgb2gray(grayImage);
end
subplot(2, 3, 1);
imshow(grayImage, [0 255]);
set(gcf, 'Name', ['Results for ' fullFileName]);
title('Original Image', 'FontSize', fontSize);
set(gcf, 'units','normalized','outerposition',[0 0 1 1]); % Maximize figure.

% Add big ripples to it.
rowVector = (1 : rows)';
period = 10; % 20 rows
amplitude = 0.5; % Magnitude of the ripples.
offset = 1 - amplitude; % How much the cosine is raised above 0.
cosVector = amplitude * (1 + cos(2 * pi * rowVector / period))/2 + offset;
ripplesImage = repmat(cosVector, [1, columns]);
subplot(2, 3, 2);
minValue = min(min(ripplesImage))
maxValue = max(max(ripplesImage))
imshow(ripplesImage, [0 maxValue]);
axis on;
title('Ripples to multiply the image by', 'FontSize', fontSize);
% Multiply the ripples by the image to get an image with periodic "noise" in it.
grayImage = ripplesImage .* double(grayImage);
minValue = min(min(grayImage))
maxValue = max(max(grayImage))
subplot(2, 3, 3);
imshow(grayImage, [0 255]);
axis on;
title('Original Image with Periodic "Noise" ripples', 'FontSize', fontSize);

% Compute the 2D fft.
frequencyImage = fftshift(fft2(grayImage));
% Take log magnitude so we can see it better in the display.
amplitudeImage = log(abs(frequencyImage));
minValue = min(min(amplitudeImage))
maxValue = max(max(amplitudeImage))
subplot(2, 3, 4);
imshow(amplitudeImage, []);
caption = sprintf('Notice the two spikes\nperpendicular to the periodic frequency');
title(caption, 'FontSize', fontSize);
axis on;
% zoom(10)

% Find the location of the big spikes.
amplitudeThreshold = 10.9;
brightSpikes = amplitudeImage > amplitudeThreshold; % Binary image.
subplot(2, 3, 5);
imshow(brightSpikes);
axis on;
title('Bright Spikes', 'FontSize', fontSize);
% Let user see the image.
promptMessage = sprintf('The image below shows the bright spikes.\nNow we will exclude the central spike.');
titleBarCaption = 'Continue?';
button = questdlg(promptMessage, titleBarCaption, 'Continue', 'Cancel', 'Continue');
if strcmpi(button, 'Cancel')
  return;
end
% Exclude the central DC spike.  Everything from row 115 to 143.
brightSpikes(115:143, :) = 0;
imshow(brightSpikes);
title('Bright spikes other than central spike', 'FontSize', fontSize);

promptMessage = sprintf('Now we will use these bright spikes to filter (mask) the spectrum.');
button = questdlg(promptMessage, titleBarCaption, 'Continue', 'Cancel', 'Continue');
if strcmpi(button, 'Cancel')
  return;
end
% Filter/mask the spectrum.
frequencyImage(brightSpikes) = 0;
% Take log magnitude so we can see it better in the display.
amplitudeImage2 = log(abs(frequencyImage));
minValue = min(min(amplitudeImage2))
maxValue = max(max(amplitudeImage2))
subplot(2, 3, 5);
imshow(amplitudeImage2, [minValue maxValue]);
axis on;
title('Spikes zeroed out', 'FontSize', fontSize);
% zoom(10)

filteredImage = ifft2(fftshift(frequencyImage));
amplitudeImage3 = abs(filteredImage);
minValue = min(min(amplitudeImage3))
maxValue = max(max(amplitudeImage3))
subplot(2, 3, 6);
imshow(amplitudeImage3, [minValue maxValue]);
title('Filtered Image', 'FontSize', fontSize);
% set(gcf, 'units','normalized','outerposition',[0 0 1 1]); % Maximize figure.
% %

[Maria]

why do i need to add ripples to my image ! its already had a periodic noise ! i just want to remove the noise from it and restor it back to its original shape ,, can u hel me please !

[Matt J]

Maria, the first part of the demo isn't adding ripples to your image. It is building its own example input image data for demonstration purposes.

[Maria]

Mr.Matt , it meant the code portion that started with : % Add big ripples to it.

Answer 2

[Youssef Khmou]

hi Maria,

Attenuating the noise means you need to design low pass filter, try this method :

 h=ones(3)/9;

You can see the frequency response of the filter h :

 figure, freqz2(h,32,32);

We take an image corrupted by AWGN :

 I=imnoise(im2double(imread('circuit.tif')),'Gaussian');

 X=filter2(h,I);

 figure, subplot(1,2,1), imshow(I), title(' noisy,v=0.05');
        subplot(1,2,2), imshow(X), title(' filtered, Low-pass');