Removing pattern and noise in an image using FFT in matlab

17
votes

I am using the clown.jpg image to be able to get rid of the obvious pattern/noise it has.

enter image description here

The first step that I did before taking FFT of the image is to rescale it a square image of powers of two (i.e. 256 x 256). Using FFT and fftshift in matlab gives the fast fourier transform with the intensities centered in the image. The following image is the result of using the previous functions mentioned.

enter image description here

I was successful to remove the pattern/noise by zeroing the "stars" manually on the FFT image as shown below:

enter image description here

Taking the IFFT I get a much better quality of picture (not shown).

The question that I have is if there is an automated way of zeroing the "stars"? I have created an interval of where to zero the images since we don't want to remove the brightest "star", the DC component, nor the low values. Such a threshold is given below:

filter = (fLog > .7*max(fLog(:)) ) | (fLog < .25*max(fLog(:)) )

where fLog is the log(1+abs(Fourier image)) and .7 and .25 are the corresponding
interval percentages.

The output mask (which I will multiply to the Fourier Image) is found below. Black corresponds to the value of 0 and white corresponds to 1. Notice that the filtering of this mask removes some "stars" and keeps some of the DC component. Obviously this method is not the best.

enter image description here

I was reading about doing a high pass filter, but that seems to remove all the outer values in the Fourier image. This is based on my previous testing (I didn't include those images).

Is there something that you recommend to highlight the high intensity values except the DC component. Ideally I would like to get the mask to look like:

enter image description here

source: http://users.accesscomm.ca/bostrum/Imaging/tips/tip1.html

In another site, it was mentioned to use "highpass and level correct the FFT data to retain only the stray dots that represent the raster pattern." I am unclear on how to do that exactly.

source: http://www.robotplanet.dk/graphics/raster_removal/

Your help will be greatly appreciated.

Here is my source code to help:

I = imread('clown.jpg'); % Read Image

% convert to grayscale
I = rgb2gray(I);

% normalize the image and conver to doubleI
I = double(mat2gray(I));

% Resize the image
I = imresize(I, [256 256]);

% get the size of the image
[rows,cols] = size(I);

% apply FFT
f = fftshift(fft2(I));

% used to plot the image
fLog = log(1 + abs(f));

% filter by a range based on fLog

filter = (fLog > .7*max(fLog(:)) ) | (fLog < .25*max(fLog(:)) );

B = abs(ifft2(f.*filter));

colormap(gray)
subplot(2,2,1),imagesc(I); title('Original Image')
subplot(2,2,2),imagesc(fLog); title('Fourier Image')
subplot(2,2,3),imagesc(filter); title('Zeroed Fourier Image')
subplot(2,2,4),imagesc(B); title('Cleaned Image')
annotation('textbox', [0 0.9 1 0.1], ...
    'String', 'Fourier Analysis on Clown Image', ...
    'EdgeColor', 'none', ...
    'HorizontalAlignment', 'center', ...
    'FontSize', 15, ...
    'FontWeight', 'bold')
2
matlabdesign-patternsimage-processingfftnoise
You know where the DC components are, why not exclude them explicitly? – Mark Ransom
This is, btw, a fairly well known technique. See, for example, books.google.com/… I haven't before seen people remove the "stars", but simply a disk near the appropriate place in the fft. – tom10
@MarkRansom Yes that is true, however, I was wondering if there was some code that automated everything – Luciano Rodriguez
@tom10 That's true that it is well known and a disc does a great job. However, if getting the right shape of all the bright values then it would make the image even better. I was simply wondering how the people on the website I mentioned were able to the mask so clearly. So I thought if they did it, maybe someone else has done something similar to it and was kind enough to share their method. – Luciano Rodriguez

2 Answers

3
votes

I tried to detect the local maximum magnitude in the frequency domain, and zero them along with their neighborhoods. It is not exactly clean, but at least realize some automatic-zero to some extent. enter image description here

My code:

I=I-mean(I(:));
f = fftshift(fft2(I));
fabs=abs(f);

roi=3;thresh=400;
local_extr = ordfilt2(fabs, roi^2, ones(roi));  % find local maximum within 3*3 range

result = (fabs == local_extr) & (fabs > thresh);

[r, c] = find(result);
for i=1:length(r)
    if (r(i)-128)^2+(c(i)-128)^2>400   % periodic noise locates in the position outside the 20-pixel-radius circle
        f(r(i)-2:r(i)+2,c(i)-2:c(i)+2)=0;  % zero the frequency components
    end
end

Inew=ifft2(fftshift(f));
imagesc(real(Inew)),colormap(gray),
0
votes

i have recently written my notch filter for my homework,i struggled for finding an example code,here is my code i hope it will helps.thanks for all.

it is an ideal notch reject filter for removing periodic noises.

I = imread('clown.jpg'); %read image
I = imresize(I, [256 256]); %resize image
[m,n] = size(I);%get size of image as m and n
[X,Y]=meshgrid(1:256,1:256); % it is a meshgrid for circle mask
filter=ones(m,n); % filter initially only ones in it
%according to notch filter equation it will find point on image is on    imaginary circle.i found circle coordinates.
for i=1:m-1
  for j=1:n-1
  d0 = i-130)^2 + (j-130)^2 <= 32^2 && (i-130)^2 + (j-130)^2 >=20^2; 
      if d0
         filter(i,j)=0;
     else
         filter(i,j)=1;
     end
   end
 end
f = fftshift(fft2(I));
G = abs(ifft2(f.*filter));
figure(1),imshow(G,[]);