Questions

1. Plot the frequency spectrum of an image, a Gaussian kernel, and the image obtained after convolution in the frequency domain, in 3D (the output should be like the surfaces shown in the sections) using the mpl_toolkits.mplot3d module. (Hint: the np.meshgrid()function will come in handy for the surface plot). Repeat the exercise for the inverse filter too.
2. Add some random noise to the lena image, blur the image with a Gaussian kernel, and then try to restore the image using an inverse filter, as shown in the corresponding example. What happens and why?
3. Use SciPy signal'sfftconvolve() function to apply a Gaussian blur on a color image in the frequency domain.
4. Use the fourier_uniform() and fourier_ellipsoid() functions of the ndimage module of SciPy to apply LPFs with box and ellipsoid kernels, respectively, on an image in the frequency domain.