使用字典学习进行图像去噪#

此示例比较了首先使用在线字典学习和各种变换方法重建浣熊脸图像的噪声片段的效果。

字典拟合在图像的失真左半部分，随后用于重建右半部分。请注意，通过拟合到未失真（即无噪声）图像可以获得更好的性能，但这里我们从不可用的假设开始。

评估图像去噪结果的一种常用方法是查看重建图像和原始图像之间的差异。如果重建是完美的，这将看起来像高斯噪声。

从图中可以看出，具有两个非零系数的正交匹配追踪 (OMP)的结果比只保留一个（边缘看起来不太突出）的结果偏差小一些。此外，它在 Frobenius 范数中更接近真实值。

最小角回归的结果偏差大得多：差异让人联想起原始图像的局部强度值。

阈值处理显然不适用于去噪，但它在这里是为了表明它可以以非常高的速度产生暗示性的输出，因此可用于对象分类等其他任务，其中性能不一定与可视化相关。

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause

生成失真图像#

import numpy as np

try:  # Scipy >= 1.10
    from scipy.datasets import face
except ImportError:
    from scipy.misc import face

raccoon_face = face(gray=True)

# Convert from uint8 representation with values between 0 and 255 to
# a floating point representation with values between 0 and 1.
raccoon_face = raccoon_face / 255.0

# downsample for higher speed
raccoon_face = (
    raccoon_face[::4, ::4]
    + raccoon_face[1::4, ::4]
    + raccoon_face[::4, 1::4]
    + raccoon_face[1::4, 1::4]
)
raccoon_face /= 4.0
height, width = raccoon_face.shape

# Distort the right half of the image
print("Distorting image...")
distorted = raccoon_face.copy()
distorted[:, width // 2 :] += 0.075 * np.random.randn(height, width // 2)

Distorting image...

显示失真图像#

import matplotlib.pyplot as plt


def show_with_diff(image, reference, title):
    """Helper function to display denoising"""
    plt.figure(figsize=(5, 3.3))
    plt.subplot(1, 2, 1)
    plt.title("Image")
    plt.imshow(image, vmin=0, vmax=1, cmap=plt.cm.gray, interpolation="nearest")
    plt.xticks(())
    plt.yticks(())
    plt.subplot(1, 2, 2)
    difference = image - reference

    plt.title("Difference (norm: %.2f)" % np.sqrt(np.sum(difference**2)))
    plt.imshow(
        difference, vmin=-0.5, vmax=0.5, cmap=plt.cm.PuOr, interpolation="nearest"
    )
    plt.xticks(())
    plt.yticks(())
    plt.suptitle(title, size=16)
    plt.subplots_adjust(0.02, 0.02, 0.98, 0.79, 0.02, 0.2)


show_with_diff(distorted, raccoon_face, "Distorted image")

Distorted image, Image, Difference (norm: 11.71)

提取参考块#

from time import time

from sklearn.feature_extraction.image import extract_patches_2d

# Extract all reference patches from the left half of the image
print("Extracting reference patches...")
t0 = time()
patch_size = (7, 7)
data = extract_patches_2d(distorted[:, : width // 2], patch_size)
data = data.reshape(data.shape[0], -1)
data -= np.mean(data, axis=0)
data /= np.std(data, axis=0)
print(f"{data.shape[0]} patches extracted in %.2fs." % (time() - t0))

Extracting reference patches...
22692 patches extracted in 0.01s.

从参考块学习字典#

from sklearn.decomposition import MiniBatchDictionaryLearning

print("Learning the dictionary...")
t0 = time()
dico = MiniBatchDictionaryLearning(
    # increase to 300 for higher quality results at the cost of slower
    # training times.
    n_components=50,
    batch_size=200,
    alpha=1.0,
    max_iter=10,
)
V = dico.fit(data).components_
dt = time() - t0
print(f"{dico.n_iter_} iterations / {dico.n_steps_} steps in {dt:.2f}.")

plt.figure(figsize=(4.2, 4))
for i, comp in enumerate(V[:100]):
    plt.subplot(10, 10, i + 1)
    plt.imshow(comp.reshape(patch_size), cmap=plt.cm.gray_r, interpolation="nearest")
    plt.xticks(())
    plt.yticks(())
plt.suptitle(
    "Dictionary learned from face patches\n"
    + "Train time %.1fs on %d patches" % (dt, len(data)),
    fontsize=16,
)
plt.subplots_adjust(0.08, 0.02, 0.92, 0.85, 0.08, 0.23)

Dictionary learned from face patches Train time 15.2s on 22692 patches

Learning the dictionary...
2.0 iterations / 125 steps in 15.16.

提取噪声块并使用字典重建它们#

from sklearn.feature_extraction.image import reconstruct_from_patches_2d

print("Extracting noisy patches... ")
t0 = time()
data = extract_patches_2d(distorted[:, width // 2 :], patch_size)
data = data.reshape(data.shape[0], -1)
intercept = np.mean(data, axis=0)
data -= intercept
print("done in %.2fs." % (time() - t0))

transform_algorithms = [
    ("Orthogonal Matching Pursuit\n1 atom", "omp", {"transform_n_nonzero_coefs": 1}),
    ("Orthogonal Matching Pursuit\n2 atoms", "omp", {"transform_n_nonzero_coefs": 2}),
    ("Least-angle regression\n4 atoms", "lars", {"transform_n_nonzero_coefs": 4}),
    ("Thresholding\n alpha=0.1", "threshold", {"transform_alpha": 0.1}),
]

reconstructions = {}
for title, transform_algorithm, kwargs in transform_algorithms:
    print(title + "...")
    reconstructions[title] = raccoon_face.copy()
    t0 = time()
    dico.set_params(transform_algorithm=transform_algorithm, **kwargs)
    code = dico.transform(data)
    patches = np.dot(code, V)

    patches += intercept
    patches = patches.reshape(len(data), *patch_size)
    if transform_algorithm == "threshold":
        patches -= patches.min()
        patches /= patches.max()
    reconstructions[title][:, width // 2 :] = reconstruct_from_patches_2d(
        patches, (height, width // 2)
    )
    dt = time() - t0
    print("done in %.2fs." % dt)
    show_with_diff(reconstructions[title], raccoon_face, title + " (time: %.1fs)" % dt)

plt.show()

Extracting noisy patches...
done in 0.00s.
Orthogonal Matching Pursuit
1 atom...
done in 0.59s.
Orthogonal Matching Pursuit
2 atoms...
done in 1.14s.
Least-angle regression
4 atoms...
done in 8.76s.
Thresholding
 alpha=0.1...
done in 0.09s.

脚本总运行时间：（0 分钟 27.032 秒）