1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
|
"""
=====================
Image Deconvolution
=====================
In this example, we deconvolve an image using the
Richardson–Lucy algorithm ([1]_, [2]_, [3]_).
The algorithm is based on a point spread function (PSF),
described as the impulse response of the
optical system. The blurred image is sharpened through a number of
iterations, which needs to be hand-tuned.
.. [1] William Hadley Richardson, "Bayesian-Based Iterative
Method of Image Restoration",
J. Opt. Soc. Am. A 27, 1593-1607 (1972), :DOI:`10.1364/JOSA.62.000055`
.. [2] https://en.wikipedia.org/wiki/Richardson%E2%80%93Lucy_deconvolution
.. [3] https://www.strollswithmydog.com/richardson-lucy-algorithm/
"""
import numpy as np
import matplotlib.pyplot as plt
import skimage as ski
from scipy.signal import convolve2d as conv2
rng = np.random.default_rng()
# Convert astronaut image to grayscale
astro = ski.color.rgb2gray(ski.data.astronaut())
# Define PSF
psf = np.ones((5, 5)) / 25
# Convolve image with the PSF to simulate a blurred image
astro_blurred = conv2(astro, psf, 'same')
# Add Poisson noise to the blurred image (https://en.wikipedia.org/wiki/Shot_noise)
max_photon_count = 1000
astro_noisy = rng.poisson(astro_blurred * max_photon_count) / max_photon_count
# Normalize noisy image
astro_noisy /= np.max(astro_noisy)
# Restore image by means of deconvolution
deconvolved_RL = ski.restoration.richardson_lucy(astro_noisy, psf, num_iter=30)
fig, ax = plt.subplots(ncols=3, figsize=(8, 5))
plt.gray()
for a in (ax[0], ax[1], ax[2]):
a.axis('off')
ax[0].imshow(astro)
ax[0].set_title('Original Data')
ax[1].imshow(astro_noisy)
ax[1].set_title('Noisy data')
ax[2].imshow(deconvolved_RL)
ax[2].set_title('Restoration using\nRichardson-Lucy')
fig.subplots_adjust(wspace=0.02, hspace=0.2, top=0.9, bottom=0.05, left=0, right=1)
plt.show()
|
