(Incomplete) Reproduction of image denoising using kernel PCA in "Learning to Find Pre-Images"

denoising.py

import numpy
import scipy.ndimage
import matplotlib.pyplot as plt

from sklearn import datasets
from sklearn import decomposition

digits = datasets.load_digits()
images = digits.images
images = map(lambda x: scipy.ndimage.zoom(x, 2, order=1), images)
d = 2 * 8

X_by_digits = [[] for i in range(10)]
for x, i in zip(images, digits.target):
    X_by_digits[i].append(x)

X_train = numpy.concatenate([X[:10] for X in X_by_digits])
X_test_without_noise = numpy.concatenate([X[10:20] for X in X_by_digits])
X_test = X_test_without_noise + 11 * numpy.random.randn(100 * d * d).reshape(100, d, d)
X_test = numpy.clip(X_test, 0, 16)

kpca = decomposition.KernelPCA(n_components=10, fit_inverse_transform=True, alpha=1)
kpca.fit(X_train.reshape(-1, d * d))

X_trans = kpca.transform(X_test.reshape(-1, d * d))
X_rec = kpca.inverse_transform(X_trans).reshape(-1, d, d)

plt.figure(figsize=(24, 8))

for i, x in enumerate(X_test_without_noise):
    col, row = 1 + i % 10, 1 + i // 10
    plt.subplot(10, 32, col + 32 * (row - 1))
    plt.imshow(x, cmap=plt.cm.gray_r)
    plt.axis('off')

for i, x in enumerate(X_test):
    col, row = 12 + i % 10, 1 + i // 10
    plt.subplot(10, 32, col + 32 * (row - 1))
    plt.imshow(x, cmap=plt.cm.gray_r)
    plt.axis('off')

for i, x in enumerate(X_rec):
    col, row = 23 + i % 10, 1 + i // 10
    plt.subplot(10, 32, col + 32 * (row - 1))
    plt.imshow(x, cmap=plt.cm.gray_r)
    plt.axis('off')

plt.suptitle("Test images before adding noise (left), test images (middle), and reconstruction of test images (right)")
plt.show()