Coding - Decoding simulation of an image

This example shows a simulation of the transmission of an image as a binary message through a gaussian white noise channel with an LDPC coding and decoding system.

# Author: Hicham Janati (hicham.janati@inria.fr)
#
# License: BSD (3-clause)


import numpy as np
from pyldpc import make_ldpc, ldpc_images
from pyldpc.utils_img import gray2bin, rgb2bin
from matplotlib import pyplot as plt
from PIL import Image

from time import time

Let’s see the image we are going to be working with

eye = Image.open("data/eye.png")
# convert it to grayscale and keep one channel
eye = np.asarray(eye.convert('LA'))[:, :, 0]

# Convert it to a binary matrix
eye_bin = gray2bin(eye)
print("Eye shape: (%s, %s)" % eye.shape)
print("Binary Eye shape: (%s, %s, %s)" % eye_bin.shape)

n = 200
d_v = 3
d_c = 4
seed = 42

Out:

Eye shape: (128, 128)
Binary Eye shape: (128, 128, 8)

First we create a small LDPC code i.e a pair of decoding and coding matrices H and G. H is a regular parity-check matrix with d_v ones per row and d_c ones per column

H, G = make_ldpc(n, d_v, d_c, seed=seed, systematic=True, sparse=True)

Now we simulate the transmission with Gaussian white noise and recover the original image via belief-propagation.

snr = 8
eye_coded, eye_noisy = ldpc_images.encode_img(G, eye_bin, snr, seed=seed)

print("Coded eye shape", eye_coded.shape)

t = time()
eye_decoded = ldpc_images.decode_img(G, H, eye_coded, snr, eye_bin.shape)
t = time() - t
print("Eye | Decoding time: ", t)
error_decoded_eye = abs(eye - eye_decoded).mean()
error_noisy_eye = abs(eye_noisy - eye).mean()

Out:

Coded eye shape (200, 2521)
Eye | Decoding time:  0.7860012054443359

With RGB images, we proceed similarly

print("\n\n")
tiger = np.asarray(Image.open("data/tiger.jpg"))
# Convert it to a binary matrix
tiger_bin = rgb2bin(tiger)
print("Tiger shape: (%s, %s, %s)" % tiger.shape)
print("Tiger Binary shape: (%s, %s, %s)" % tiger_bin.shape)


tiger_coded, tiger_noisy = ldpc_images.encode_img(G, tiger_bin, snr, seed=seed)

print("Coded Tiger shape", tiger_coded.shape)

t = time()
tiger_decoded = ldpc_images.decode_img(G, H, tiger_coded, snr, tiger_bin.shape)
t = time() - t
print("Tiger | Decoding time: ", t)

error_decoded_tiger = abs(tiger - tiger_decoded).mean()
error_noisy_tiger = abs(tiger_noisy - tiger).mean()


titles_eye = ["Original", "Noisy | Err = %.3f %%" % error_noisy_eye,
              "Decoded | Err = %.3f %%" % error_decoded_eye]
titles_tiger = ["Original", "Noisy | Err = %.3f %%" % error_noisy_tiger,
                "Decoded | Err = %.3f %%" % error_decoded_tiger]
all_imgs = [[eye, eye_noisy, eye_decoded], [tiger, tiger_noisy, tiger_decoded]]
f, axes = plt.subplots(2, 3, figsize=(18, 12))
for ax_row, titles, img_list, cmap in zip(axes, [titles_eye, titles_tiger],
                                          all_imgs, ["gray", None]):
    for ax, data, title in zip(ax_row, img_list, titles):
        ax.imshow(data, cmap=cmap)
        ax.set_title(title, fontsize=20)
        ax.set_xticks([])
        ax.set_yticks([])
plt.tight_layout()
plt.show()

Out:

Tiger shape: (128, 128, 3)
Tiger Binary shape: (128, 128, 24)
Coded Tiger shape (200, 7562)
Tiger | Decoding time:  2.2028489112854004
/Users/hichamjanati/Documents/github/pyldpc/examples/plot_image_transmission.py:101: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
  plt.show()

Estimated memory usage: 168 MB