MATLAB image processing - cosine noise removal in image (with code)

Problem description

There are the following images after adding noise ：

It is obvious from the picture that x A sinusoidal noise is superimposed in the direction , To denoise it , It is easier to map to the frequency domain , Observe where the noise occurs , Filter in frequency domain , Finally, the inverse Fourier transform .

Fourier transform

Fourier transform the original image to get ：

It's hard to see from the picture above , Map it to x In the direction of , Get a one-dimensional distribution and get ：

It can be seen that there are three spikes , The middle peak is useful information , What we need to keep , The two spikes nearby are caused by noise , So you can use Band stop filter Filter out the two peak noises .

Band stop filter

The two band stop filters constructed are shown in the figure below , The peak values filtered out are respectively 120 and 138 Noise at .
Use a band stop filter to multiply the projection of the Fourier spectrum , The range of band stop filter value is 0~1, The darker it is, the closer it is 0, The brighter it is, the closer it is 1.

wave filtering

Use the above filter to filter the Fourier transform spectrum , And in x Visualize in the direction to get ：

It can be seen that the peak value is 120 and 138 The noise has been filtered out .

result

The inverse Fourier transform is performed to obtain ：

It can be seen that , The image obtained after inverse Fourier transform , There is some picture distortion , The reason may be the operation of reducing the spectrum of the image from two dimensions to one dimension , In some places where there is no noise , The filtering operation is also carried out , So there will be a certain loss of information . If on the global information , That is to say, denoising on two-dimensional information should get better results .

improvement

Fine filtering of the square area in the figure should get better results .

Code

close all
f=imread('grid.bmp');
[M,N,~] = size(f); %f Is a noisy image 
F = fftshift(fft2(f)); %  Image frequency domain 
figure;plot(abs(F(M/2+1,:))); % x Direction transverse line 
%  structure n Step Butterworth trap , You can modify D0 and n Get better results .
u = 0:(M-1);
v = 0:(N-1);
[V,U] = meshgrid(v,u);
D0 = 7;
n = 1;
v0 = 120;
v1 = 138;
D1 = abs(V-v0);
D2 = abs(V-v1);
H = 1./(1+(D0^2./(D1.*D2)).^n);
figure;imshow(H,[])
%  wave filtering 
G = fftshift(F.*H);
figure;plot(abs(F.*H(M/2+1,:))); % x Direction transverse line 
g = real(ifft2(G));

figure;
subplot(121); imshow(f,[]);
subplot(122),imshow(g,[]);