小波去噪

小波去噪依赖于图像的小波表示。高斯噪声在小波域中通常表现为较小的值，可以通过将低于给定阈值的系数设置为零（硬阈值）或将所有系数向零方向收缩一定量（软阈值）来去除。

在这个例子中，我们展示了两种不同的方法来进行小波系数阈值选择：BayesShrink 和 VisuShrink。

VisuShrink

VisuShrink 方法对所有小波细节系数采用单一的通用阈值。该阈值旨在高概率地去除加性高斯噪声，这往往会导致图像过度平滑。通过指定一个小于真实噪声标准差的 sigma，可以获得更视觉上令人满意的结果。

BayesShrink

BayesShrink 算法是一种自适应的小波软阈值方法，其中为每个小波子带估计一个独特的阈值。这通常会带来比单一阈值更好的效果。

Estimated Gaussian noise standard deviation = 0.11570833129990649
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers). Got range [-0.061167435808144044..0.8523305913105099].
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers). Got range [-0.011393704460198389..0.8154777398248884].
Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers). Got range [-0.07176196160470502..0.9176973273707948].

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'
    'PSNR=%0.4g' % psnr_visushrink
)
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'
    'PSNR=%0.4g' % psnr_visushrink2
)
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'
    'PSNR=%0.4g' % psnr_visushrink4
)
fig.tight_layout()

plt.show()