MATLAB: Image Enhancement using Fast fourier transform

Question

I need to enhance my image using fast fourier transform. This has to be done first by dividing the image into 32×32 pixel blocks. For each block, fft is applied and is multipled by some factor which is nothing but its absolute value raised to the power of 0.5. After this we need to inverse transform it back for each block.

The enhancement result of each block combined all together forms the enhanced image.

Guys I'm not getting the result. Please anyone sort this out for me with code.

Answer 1

I don't understand. First of all because you're applying this only to very small blocks, there are essentially no low frequencies in the FT. Then you multiply by 0.5 so this suppresses all frequencies in there, which I said will be mostly high frequencies, not low frequencies. So essentially you're suppressing high frequencies and not doing to much to low frequencies (because they're not there). I guess this could be an "enhancement" if you consider suppression of high frequencies, which often include the noisier part of the signal, to be enhancement. Usually though people mean a high frequency boost when they say enhancement. Anyway, you can do the whole thing more effectively and with greater precision over the frequency cutoff with just one Fourier Transform on the whole image, instead of a bunch of little ones. I have a demo for that, if you're interested:

% 2D FFT Demo
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
imtool close all;  % Close all imtool figures.
clear;  % Erase all existing variables.
workspace;  % Make sure the workspace panel is showing.
format longg;
format compact;
fontSize = 20;
% Change the current folder to the folder of this m-file.
if(~isdeployed)
  cd(fileparts(which(mfilename)));
end
  
% Check that user has the Image Processing Toolbox installed.
hasIPT = license('test', 'image_toolbox');
if ~hasIPT
  % User does not have the toolbox installed.
  message = sprintf('Sorry, but you do not seem to have the Image Processing Toolbox.\nDo you want to try to continue anyway?');
  reply = questdlg(message, 'Toolbox missing', 'Yes', 'No', 'Yes');
  if strcmpi(reply, 'No')
    % User said No, so exit.
    return;
  end
end
% 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
% Read in image.
grayImage = imread('cameraman.tif');
[rows columns numberOfColorChannels] = size(grayImage)
if numberOfColorChannels > 1
  grayImage = rgb2gray(grayImage);
end
% Display original grayscale image.
subplot(2, 2, 1);
imshow(grayImage)
title('Original Gray Scale Image', 'FontSize', fontSize)
% Perform 2D FFTs
fftOriginal = fft2(double(grayImage));
shiftedFFT = fftshift(fftOriginal);
subplot(2, 2, 2);
imshow(real(shiftedFFT));
title('Real Part of Spectrum', 'FontSize', fontSize)
subplot(2, 2, 3);
imshow(imag(shiftedFFT));
title('Imaginary Part of Spectrum', 'FontSize', fontSize)
% Display magnitude and phase of 2D FFTs
subplot(2, 2, 4);
imshow(log(abs(shiftedFFT)),[]);
colormap gray
title('Log Magnitude of Spectrum', 'FontSize', fontSize)
% Enlarge figure to full screen.

set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Now convolve with a 2D rect function.
figure;
rectWidth = 10;
rectHeight = 5;
kernel = ones(rectHeight, rectWidth) / (rectHeight * rectWidth);
% Display it
subplot(2, 2, 1);
k = padarray(kernel, [3, 3]); % Just for display.
imshow(k, []);
axis on;
title('Kernel', 'FontSize', fontSize)
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Convolve kernel (box filter) with the image
filteredImage = conv2(double(grayImage), kernel, 'same');
% Display filtered image.
subplot(2, 2, 2);
imshow(filteredImage,[]);
title('Filtered Image', 'FontSize', fontSize)
% Perform 2D FFT on the filtered image to see its spectrum.
% We expect to see a sinc multiplication effect.
% It should look like the original but with a sinc pattern overlaid on it.
fftFiltered = fft2(double(filteredImage));
shiftedFFT = fftshift(fftFiltered);
% Display magnitude of the 2D FFT of the filtered image.
subplot(2, 2, 3);
imshow(log(abs(shiftedFFT)),[]);
colormap gray
title('Log Magnitude of Spectrum - Note sinc multiplication', 'FontSize', fontSize)