The Conjugate Gradient (CG) is an algorithm solving linear equation systems in an iterative manner. In this notebook it used to demonstrate de-blurring of an image suffering from optical defocus.
last update: 02/05/2022
At the beginning we load an picture showing the Swiss alps which crisp high frequency features. To mimic optical defocus, we convolve the ground-truth image with the Point-Spread Function (PSF), which represents the impulse response of an objective lens and is typically used to model the interferrence of propagating light waves.
from pathlib import Path
import imageio
from scipy.ndimage import convolve
from utils.gibson_lanni import create_psf_kernel
psf_kernel = create_psf_kernel(size=64)[..., -23][16:-16, 16:-16]
path = Path('.') / 'img' / 'alps.png'
gimg = imageio.imread(str(path)).astype('float')
psf_conv = lambda img, kernel=psf_kernel: convolve(img, kernel, mode='reflect', cval=0.0, origin=0)
# blur image
bimg = psf_conv(gimg)
import matplotlib.pyplot as plt
%matplotlib inline
fig, axs = plt.subplots(nrows=1, ncols=3, figsize=(25, 5))
axs[0].imshow(gimg, cmap='gray')
axs[1].imshow(psf_kernel, cmap='gray')
axs[2].imshow(bimg, cmap='gray')
axs[0].set_title('Ground-truth', fontsize=24)
axs[1].set_title('Point-Spread-Function (PSF)', fontsize=24)
axs[2].set_title('Defocused image', fontsize=24)
axs[0].tick_params(top=False, bottom=False, left=False, right=False, labelleft=False, labelbottom=False)
axs[1].tick_params(top=False, bottom=False, left=False, right=False, labelleft=False, labelbottom=False)
axs[2].tick_params(top=False, bottom=False, left=False, right=False, labelleft=False, labelbottom=False)
fig.tight_layout()