How to use 2D FFT to remove horizontal noise from the image

Sorry a beginner here. I have no clue on how to remove the horizontal noise from the images using the 2D FFT method. I've found some code online but it doesn't seem to work can anyone help me. Thank you.

This is the picture with amplified noise

This is the original picture with the noise

Answer 1

[Mathieu NOE]

hello

you can start with simple 2D filtering

here some examples you can easily try once you have dowloaded those functions : smooth2a and smoothn from here

smooth2a - File Exchange - MATLAB Central (mathworks.com)

smoothn - File Exchange - MATLAB Central (mathworks.com)

Result with smooth2a (notice you can have different smoothing factor for x and y directions)

Result with smoothn

demo code

inpict = im2double(rgb2gray(imread('image.png')));

figure(1)
outpict = smooth2a(inpict,5,3);
subplot(1,2,1),imagesc(inpict)
subplot(1,2,2),imagesc(outpict)

figure(2)
outpict = smoothn(inpict);
subplot(1,2,1),imagesc(inpict)
subplot(1,2,2),imagesc(outpict)

[Jensen Lee]

Hi Mathieu NOE,

Thank you for your answer, but the horizontal streaks pattern type of noise is still present in the image. Any idea on how to remove/reduce it. Thanks in advance.

[Mathieu NOE]

there is maybe a solution here

Remove periodic noise pattern from image - MATLAB Answers - MATLAB Central (mathworks.com)

[Mathieu NOE]

maybe this ?

see final result on the far right picture

tx to the Rice University for providing the low pass filter code

filename = 'image.png';

inpict = im2double(rgb2gray(imread(filename)));

% remove mean along dimension 2 (that will remove already a big portion of
% the streaks)
m = mean(inpict,2);
inpict2 = inpict - m*ones(1,b);

spec_img = fftshift(fft2(inpict2));
sze = size(spec_img);

% low pass elliptical filering of the input image (to remove further the
% salt pepper noise) - adjust filter cut off and order to your own
% preferences
sze = size(spec_img);
cutoff1 = 0.5;
cutoff2 = 0.5;
n = 4;
f = EFilter(sze, cutoff1, cutoff2, n);

% apply filter
spec_img = spec_img.*f;

% generated backward the output image by inverse fft
outpict = real(ifft2(ifftshift(spec_img)));

figure(1)
subplot(1,3,1),imshow(inpict)
subplot(1,3,2),imshow(inpict2)
subplot(1,3,3),imshow(outpict)


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function varargout = EFilter(sze, cutoffM, cutoffm, n, varargin)

%EFILTER constructs an elliptical lowpass filter Butterworth filter
%   E = EFILTER(Size, cutoffM, cutoffm, n) designs an Nth order elliptical
%   lowpass digital Butterworth filter where Size is a two element 
%   [rows, cols] vector specifying the size of the filter to construct, 
%   cutoffM and cutoffm, the cutoff freqency on the major and minor
%   axes are 0 < cutoff <= 1.
%
%   If E = EFilter(Size, cutoffM, cutoffm, n, alpha), where alpha is an angle
%   in radians, it will return and plot an elliptical filter rotated
%   counter-clockwise through alpha.
%
%   If E = EFilter(Size, cutoffM, cutoffm, n, alpha, xoff, yoff), where xoff
%   and yoff are offsets in the x and y direction, it will return and
%   plot an eliptical filter which is offset by the specified amount.
%   An offset of 0 corresponds to the center and an offset of 1
%   corresponds to the edge of the filter. A positive offset shifts the
%   filter in the positive direction.
%
%   Calling EFilter(...) without assigning the output variable
%   plots the 3D surface described by the function.

% Katie Streit   [e-mail]
% ELEC 301
% Rice University
%
% December 2001

% Much of this code was based on Peter Kovesi's  ([e-mail])
% Matlab function for a lowpass Butterworth filter.

if nargin == 4
alpha = 0;
offx = 0;
offy = 0;
elseif nargin == 5
offx = 0;
offy = 0;
alpha = varargin{1};
elseif nargin == 7
alpha = varargin{1};
offx = varargin{2};
offy = varargin{3};
else
	error('Invalid number of input arguments');
end

    if nargout > 1
        error('Invalid number of output arguments');
    end

    if cutoffM < 0 | cutoffM > 1
	error('cutoffM frequency must be between 0 and 1');
    end
    
    if cutoffm < 0 | cutoffm > 1
        error('cutoffm frequency must be between 0 and 1');
    end  
      
    if rem(n,1) ~= 0 | n < 1
	error('n must be an integer >= 1');
    end
    

%%extracts the sizes from sze 
rows = sze(1);
cols = sze(2);

%x and y matrices normalized to +/-.5 and an offset of offx or offy
x =  ((((ones(rows,1) * [1:cols])-offx*rows/2)  - (fix(cols/2)+1))/cols);
y =  ((([1:rows]' * ones(1,cols))-offy*rows/2) - (fix(rows/2)+1))/rows;

%applies a linear transformation to rotate through alpha. Note that it takes
% uses negative alpha, which is caused by x and y being independent matrices.
x2 = (x*cos(alpha) - y*sin(-alpha));
y2 = (x*sin(-alpha) + y*cos(alpha));

%constructs an elliptical cone (defined by a and b) of height r on each at 
%each elliptical ring. (r is effectively the "radius")
%r = sqrt(((x2/a).^2 + (y2/b).^2));

%Designs the filter
%f = 1./(1.0 + (r./cutoff).^(2*n));

a = cutoffM/2;
b = cutoffm/2;

f = 1./(1+((x2/(a)).^2 + (y2/(b)).^2).^n);

if nargout > 0
  varargout{1} = f;
else
  %Plots a normalized (+/- 1), interpolated 3D image of the filter
  surf([-1:2/(cols-1):1],[-1:2/(rows-1):1], f);
  shading interp;
  title('Elliptical Butterworth filter');
  xlabel('x');
  ylabel('y');
  zlabel('intensity');
  grid on;
end

end

[Mathieu NOE]

well , that works too : combining the mean + averaging gives something very similar indeed with a very short code

inpict = im2double(rgb2gray(imread('image.png')));
[a,b] = size(inpict);

% remove mean along dimension 2 (that will remove already a big portion of
% the streaks)
m = mean(inpict,2);
inpict2 = inpict - m*ones(1,b);

outpict = smoothn(inpict2,0.3); % add a bit of salt / pepper denoising
% outpict = smooth2a(inpict2,3,3); % add a bit of salt / pepper denoising

figure(1)
subplot(1,2,1),imshow(inpict)
subplot(1,2,2),imshow(outpict)

[Jensen Lee]

Hi Mathieu NOE,

Sorry for the late reply. Thank you for your answer.

[Mathieu NOE]

No problem

as always, my pleasure !