How to perform 2 dimensional circular convolution

We have 'conv' and 'conv2' functions in matlab to find 1-D and 2-D linear convolution.

But for circular convolution we have only 'cconv' for 1-D convolution. Is there 2-D circular convolution function in matlab or there is any way to acheive 2-D circular convolution in MATLAB.

I tried using 'conv2(A,B,'same'), but it is not same as 2-D circular convolution.

Answer 1

[Matt J]

function z=cyconv(x,y)
%Non-Fourier domain cyclic convolution.
%
%  z=cyconv(x,y)
%
%Note: y can be shorter in any of its dimensions than x and will be
%zero-padded implicitly.

 xsiz=num2cell(size(x));
 ysiz=num2cell(size(y));

 subs=cellfun(@(n,m)[n-(m-2):n,1:n],xsiz, ysiz,'uni',0);
 
 x=x(subs{:});
 
 z=convn(x,y,'valid');

[Palguna Gopireddy]

Thank you so much.

Answer 2

[Matt J]

Using FFTs

out = ifft2(fft2(A).*fft2(B));

[Ahmed]

this is better

[Matt J]

@Ahmed if by better, you mean faster, then that won't always be true. If you are convolving a large array with a short kernel, it is often faster to work in the non-Fourier domain. Example:

n=5000;
A=rand(n);
B=rand(5);

tic;
  out1 = real(ifft2(fft2(A).*fft2(B,n,n)));
toc;

Elapsed time is 0.786392 seconds.

tic;
  out2 = cyconv(A,B);
toc;

Elapsed time is 0.284089 seconds.

percentDifference=norm(out1-out2,'inf')/norm(out1,'inf')*100

percentDifference = 8.2314e-14

function z=cyconv(x,y)
%Non-Fourier domain cyclic convolution
%
%  z=cyconv(x,y)

 xsiz=num2cell(size(x));
 ysiz=num2cell(size(y));

 subs=cellfun(@(n,m)[n-(m-2):n,1:n],xsiz, ysiz,'uni',0);

 x=x(subs{:});

 z=convn(x,y,'valid');
 
end