Frequency domain Gaussian blur filter with numpy fft

The following code block shows how to apply a Gaussian filter in the frequency domain using the convolution theorem and numpy fft (since in the frequency domain it is simply multiplication):

pylab.figure(figsize=(20,15))
pylab.gray() # show the filtered result in grayscale
im = np.mean(imread('../images/lena.jpg'), axis=2)
gauss_kernel = np.outer(signal.gaussian(im.shape[0], 5), signal.gaussian(im.shape[1], 5))
freq = fp.fft2(im)
assert(freq.shape == gauss_kernel.shape)
freq_kernel = fp.fft2(fp.ifftshift(gauss_kernel))
convolved = freq*freq_kernel # by the convolution theorem, simply multiply in the frequency domain
im1 = fp.ifft2(convolved).real
pylab.subplot(2,3,1), pylab.imshow(im), pylab.title('Original Image',
size=20), pylab.axis('off')
pylab.subplot(2,3,2), pylab.imshow(gauss_kernel), pylab.title('Gaussian Kernel', size=20)
pylab.subplot(2,3,3), pylab.imshow(im1) # the imaginary part is an artifact
pylab.title('Output Image', size=20), pylab.axis('off')
pylab.subplot(2,3,4), pylab.imshow( (20*np.log10( 0.1 + fp.fftshift(freq))).astype(int))
pylab.title('Original Image Spectrum', size=20), pylab.axis('off')
pylab.subplot(2,3,5), pylab.imshow( (20*np.log10( 0.1 +
fp.fftshift(freq_kernel))).astype(int))
pylab.title('Gaussian Kernel Spectrum', size=20), pylab.subplot(2,3,6)
pylab.imshow( (20*np.log10( 0.1 + fp.fftshift(convolved))).astype(int))
pylab.title('Output Image Spectrum', size=20), pylab.axis('off')
pylab.subplots_adjust(wspace=0.2, hspace=0)
pylab.show()

The following screenshot shows the output of the preceding code, the original lena image, the kernel, and the output image obtained after convolution, both in the spatial and frequency domains: