小波去噪

小波去噪依賴於影像的小波表示。高斯雜訊往往以小值表示在小波域中，並且可以透過將低於給定閾值的係數設定為零（硬閾值處理）或將所有係數朝零方向縮小給定的量（軟閾值處理）來移除。

在此範例中，我們說明兩種不同的小波係數閾值選擇方法：BayesShrink 和 VisuShrink。

VisuShrink

VisuShrink 方法對所有小波細節係數採用單一的通用閾值。此閾值旨在高機率地移除加性高斯雜訊，這往往會導致影像外觀過於平滑。透過指定小於真實雜訊標準差的 sigma，可以獲得更視覺上令人滿意的結果。

BayesShrink

BayesShrink 演算法是一種小波軟閾值處理的自適應方法，其中針對每個小波子頻帶估計唯一的閾值。這通常會比單一閾值所能獲得的結果有所改進。

Estimated Gaussian noise standard deviation = 0.1179913573463555
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers). Got range [-0.02308914292237688..0.852072291119182].
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers). Got range [-0.05623687585380091..0.9301300180245746].

import matplotlib.pyplot as plt

from skimage.restoration import denoise_wavelet, estimate_sigma
from skimage import data, img_as_float
from skimage.util import random_noise
from skimage.metrics import peak_signal_noise_ratio


original = img_as_float(data.chelsea()[100:250, 50:300])

sigma = 0.12
noisy = random_noise(original, var=sigma**2)

fig, ax = plt.subplots(nrows=2, ncols=3, figsize=(8, 5), sharex=True, sharey=True)

plt.gray()

# Estimate the average noise standard deviation across color channels.
sigma_est = estimate_sigma(noisy, channel_axis=-1, average_sigmas=True)
# Due to clipping in random_noise, the estimate will be a bit smaller than the
# specified sigma.
print(f'Estimated Gaussian noise standard deviation = {sigma_est}')

im_bayes = denoise_wavelet(
    noisy,
    channel_axis=-1,
    convert2ycbcr=True,
    method='BayesShrink',
    mode='soft',
    rescale_sigma=True,
)
im_visushrink = denoise_wavelet(
    noisy,
    channel_axis=-1,
    convert2ycbcr=True,
    method='VisuShrink',
    mode='soft',
    sigma=sigma_est,
    rescale_sigma=True,
)

# VisuShrink is designed to eliminate noise with high probability, but this
# results in a visually over-smooth appearance.  Repeat, specifying a reduction
# in the threshold by factors of 2 and 4.
im_visushrink2 = denoise_wavelet(
    noisy,
    channel_axis=-1,
    convert2ycbcr=True,
    method='VisuShrink',
    mode='soft',
    sigma=sigma_est / 2,
    rescale_sigma=True,
)
im_visushrink4 = denoise_wavelet(
    noisy,
    channel_axis=-1,
    convert2ycbcr=True,
    method='VisuShrink',
    mode='soft',
    sigma=sigma_est / 4,
    rescale_sigma=True,
)

# Compute PSNR as an indication of image quality
psnr_noisy = peak_signal_noise_ratio(original, noisy)
psnr_bayes = peak_signal_noise_ratio(original, im_bayes)
psnr_visushrink = peak_signal_noise_ratio(original, im_visushrink)
psnr_visushrink2 = peak_signal_noise_ratio(original, im_visushrink2)
psnr_visushrink4 = peak_signal_noise_ratio(original, im_visushrink4)

ax[0, 0].imshow(noisy)
ax[0, 0].axis('off')
ax[0, 0].set_title(f'Noisy\nPSNR={psnr_noisy:0.4g}')
ax[0, 1].imshow(im_bayes)
ax[0, 1].axis('off')
ax[0, 1].set_title(f'Wavelet denoising\n(BayesShrink)\nPSNR={psnr_bayes:0.4g}')
ax[0, 2].imshow(im_visushrink)
ax[0, 2].axis('off')
ax[0, 2].set_title(
    'Wavelet denoising\n(VisuShrink, $\\sigma=\\sigma_{est}$)\n'
    f'PSNR={psnr_visushrink:0.4g}'
)
ax[1, 0].imshow(original)
ax[1, 0].axis('off')
ax[1, 0].set_title('Original')
ax[1, 1].imshow(im_visushrink2)
ax[1, 1].axis('off')
ax[1, 1].set_title(
    'Wavelet denoising\n(VisuShrink, $\\sigma=\\sigma_{est}/2$)\n'
    f'PSNR={psnr_visushrink2:0.4g}'
)
ax[1, 2].imshow(im_visushrink4)
ax[1, 2].axis('off')
ax[1, 2].set_title(
    'Wavelet denoising\n(VisuShrink, $\\sigma=\\sigma_{est}/4$)\n'
    f'PSNR={psnr_visushrink4:0.4g}'
)
fig.tight_layout()

plt.show()