MATLAB: Filter in the frequency domain that is capable of attenuating periodic additive noise

filterfilter designfrequencyhistogramImage Processing Toolbox

i need code and procedure for filter in the frequency domain that is capable of attenuating periodic additive noise….

Best Answer

Take the FFT, and look for spikes - these represent significant periodic signal in your input. Then zero those spikes out, or attenuate them by multiplying by some factor less than 1. Here's my demo on a 2D image:
% 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.
% %
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