I wanted to take the convolution M different images (stored in an M x n x n) matrix with the same kernel in the Fourier domain, but I couldn’t figure out how to run fft2 on the second and third dimension of that matrix (computing a bunch of 2D FFTs in a single matlab call).
Turns out fft2 is a really simple function (type edit fft2 to see how it works) which involves calling fft on dimension 1 of an image, and then again on dimension 2. To take the 2d fft of all the images stored in the images matrix, then, proceed as follows:
imagesfft2 = fft(fft(images,,2),,3);
To convolve the kernel with the images, you need to multiply element wise with the 2d fft of the kernel. This is done cleanly using reshape and bsxfun:
kernfft2 = fft2(kern); kernfft2 = reshape(kernfft2,[1,size(kernfft2)]) imagesfilt = bsxfun(@times,imagesfft2,kernfft2);
And to bring back to the image domain:
imagesconv = ifft(ifft(imagesfilt,,2),,3);