Convolutional Autoencoder

Sticking with the MNIST dataset, let's improve our autoencoder's performance using convolutional layers. Again, loading modules and the data.



In [4]:

    
%matplotlib inline

import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt



In [5]:

    
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets('MNIST_data', validation_size=0)









    



Extracting MNIST_data/train-images-idx3-ubyte.gz
Extracting MNIST_data/train-labels-idx1-ubyte.gz
Extracting MNIST_data/t10k-images-idx3-ubyte.gz
Extracting MNIST_data/t10k-labels-idx1-ubyte.gz



In [6]:

    
img = mnist.train.images[2]
plt.imshow(img.reshape((28, 28)), cmap='Greys_r')









    Out[6]:





<matplotlib.image.AxesImage at 0x7f8ea6a82b38>

Network Architecture

The encoder part of the network will be a typical convolutional pyramid. Each convolutional layer will be followed by a max-pooling layer to reduce the dimensions of the layers. The decoder though might be something new to you. The decoder needs to convert from a narrow representation to a wide reconstructed image. For example, the representation could be a 4x4x8 max-pool layer. This is the output of the encoder, but also the input to the decoder. We want to get a 28x28x1 image out from the decoder so we need to work our way back up from the narrow decoder input layer. A schematic of the network is shown below.

Here our final encoder layer has size 4x4x8 = 128. The original images have size 28x28 = 784, so the encoded vector is roughly 16% the size of the original image. These are just suggested sizes for each of the layers. Feel free to change the depths and sizes, but remember our goal here is to find a small representation of the input data.

What's going on with the decoder

Okay, so the decoder has these "Upsample" layers that you might not have seen before. First off, we'll discuss a bit what these layers aren't. Usually, we see transposed convolution layers used to increase the width and height of the layers. They work almost exactly the same as convolutional layers, but in reverse. A stride in the input layer results in a larger stride in the transposed convolution layer. For example, if you have a 3x3 kernel, a 3x3 patch in the input layer will be reduced to one unit in a convolutional layer. Comparatively, one unit in the input layer will be expanded to a 3x3 path in a transposed convolution layer. The TensorFlow API provides us with an easy way to create the layers, tf.nn.conv2d_transpose.

However, transposed convolution layers can lead to artifacts in the final images, such as checkerboard patterns. This is due to overlap in the kernels which can be avoided by setting the stride and kernel size equal. In this Distill article from Augustus Odena, et al, the authors show that these checkerboard artifacts can be avoided by resizing the layers using nearest neighbor or bilinear interpolation (upsampling) followed by a convolutional layer. In TensorFlow, this is easily done with tf.image.resize_images, followed by a convolution. Be sure to read the Distill article to get a better understanding of deconvolutional layers and why we're using upsampling.



In [8]:

    
inputs_ = tf.placeholder(tf.float32, (None, 28, 28, 1), name='inputs')
targets_ = tf.placeholder(tf.float32, (None, 28, 28, 1), name='targets')

### Encoder
conv1 = tf.layers.conv2d(inputs_, 16, (3,3), padding='same', activation=tf.nn.relu)
# Now 28x28x16
maxpool1 = tf.layers.max_pooling2d(conv1, (2,2), (2,2), padding='same')
# Now 14x14x16
conv2 = tf.layers.conv2d(maxpool1, 8, (3,3), padding='same', activation=tf.nn.relu)
# Now 14x14x8
maxpool2 = tf.layers.max_pooling2d(conv2, (2,2), (2,2), padding='same')
# Now 7x7x8
conv3 = tf.layers.conv2d(maxpool2, 8, (3,3), padding='same', activation=tf.nn.relu)
# Now 7x7x8
encoded = tf.layers.max_pooling2d(conv3, (2,2), (2,2), padding='same')
# Now 4x4x8

### Decoder
upsample1 = tf.image.resize_nearest_neighbor(encoded, (7,7))
# Now 7x7x8
conv4 = tf.layers.conv2d(upsample1, 8, (3,3), padding='same', activation=tf.nn.relu)
# Now 7x7x8
upsample2 = tf.image.resize_nearest_neighbor(conv4, (14,14))
# Now 14x14x8
conv5 = tf.layers.conv2d(upsample2, 8, (3,3), padding='same', activation=tf.nn.relu)
# Now 14x14x8
upsample3 = tf.image.resize_nearest_neighbor(conv5, (28,28))
# Now 28x28x8
conv6 = tf.layers.conv2d(upsample3, 16, (3,3), padding='same', activation=tf.nn.relu)
# Now 28x28x16

logits = tf.layers.conv2d(conv6, 1, (3,3), padding='same', activation=None)
#Now 28x28x1

decoded = tf.nn.sigmoid(logits, name='decoded')

loss = tf.nn.sigmoid_cross_entropy_with_logits(labels=targets_, logits=logits)
cost = tf.reduce_mean(loss)
opt = tf.train.AdamOptimizer(0.001).minimize(cost)

Training

As before, here we'll train the network. Instead of flattening the images though, we can pass them in as 28x28x1 arrays.



In [9]:

    
sess = tf.Session()



In [10]:

    
epochs = 10
batch_size = 200
sess.run(tf.global_variables_initializer())
for e in range(epochs):
    for ii in range(mnist.train.num_examples//batch_size):
        batch = mnist.train.next_batch(batch_size)
        imgs = batch[0].reshape((-1, 28, 28, 1))
        batch_cost, _ = sess.run([cost, opt], feed_dict={inputs_: imgs,
                                                         targets_: imgs})

        print("Epoch: {}/{}...".format(e+1, epochs),
              "Training loss: {:.4f}".format(batch_cost))









    



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In [11]:

    
fig, axes = plt.subplots(nrows=2, ncols=10, sharex=True, sharey=True, figsize=(20,4))
in_imgs = mnist.test.images[:10]
reconstructed = sess.run(decoded, feed_dict={inputs_: in_imgs.reshape((10, 28, 28, 1))})

for images, row in zip([in_imgs, reconstructed], axes):
    for img, ax in zip(images, row):
        ax.imshow(img.reshape((28, 28)), cmap='Greys_r')
        ax.get_xaxis().set_visible(False)
        ax.get_yaxis().set_visible(False)


fig.tight_layout(pad=0.1)



In [12]:

    
sess.close()

Denoising

As I've mentioned before, autoencoders like the ones you've built so far aren't too useful in practive. However, they can be used to denoise images quite successfully just by training the network on noisy images. We can create the noisy images ourselves by adding Gaussian noise to the training images, then clipping the values to be between 0 and 1. We'll use noisy images as input and the original, clean images as targets. Here's an example of the noisy images I generated and the denoised images.

Denoising autoencoder

Since this is a harder problem for the network, we'll want to use deeper convolutional layers here, more feature maps. I suggest something like 32-32-16 for the depths of the convolutional layers in the encoder, and the same depths going backward through the decoder. Otherwise the architecture is the same as before



In [13]:

    
inputs_ = tf.placeholder(tf.float32, (None, 28, 28, 1), name='inputs')
targets_ = tf.placeholder(tf.float32, (None, 28, 28, 1), name='targets')

### Encoder
conv1 = tf.layers.conv2d(inputs_, 32, (3,3), padding='same', activation=tf.nn.relu)
# Now 28x28x32
maxpool1 = tf.layers.max_pooling2d(conv1, (2,2), (2,2), padding='same')
# Now 14x14x32
conv2 = tf.layers.conv2d(maxpool1, 32, (3,3), padding='same', activation=tf.nn.relu)
# Now 14x14x32
maxpool2 = tf.layers.max_pooling2d(conv2, (2,2), (2,2), padding='same')
# Now 7x7x32
conv3 = tf.layers.conv2d(maxpool2, 16, (3,3), padding='same', activation=tf.nn.relu)
# Now 7x7x16
encoded = tf.layers.max_pooling2d(conv3, (2,2), (2,2), padding='same')
# Now 4x4x16

### Decoder
upsample1 = tf.image.resize_nearest_neighbor(encoded, (7,7))
# Now 7x7x16
conv4 = tf.layers.conv2d(upsample1, 16, (3,3), padding='same', activation=tf.nn.relu)
# Now 7x7x16
upsample2 = tf.image.resize_nearest_neighbor(conv4, (14,14))
# Now 14x14x16
conv5 = tf.layers.conv2d(upsample2, 32, (3,3), padding='same', activation=tf.nn.relu)
# Now 14x14x32
upsample3 = tf.image.resize_nearest_neighbor(conv5, (28,28))
# Now 28x28x32
conv6 = tf.layers.conv2d(upsample3, 32, (3,3), padding='same', activation=tf.nn.relu)
# Now 28x28x32

logits = tf.layers.conv2d(conv6, 1, (3,3), padding='same', activation=None)
#Now 28x28x1

decoded = tf.nn.sigmoid(logits, name='decoded')

loss = tf.nn.sigmoid_cross_entropy_with_logits(labels=targets_, logits=logits)
cost = tf.reduce_mean(loss)
opt = tf.train.AdamOptimizer(0.001).minimize(cost)



In [14]:

    
sess = tf.Session()



In [15]:

    
epochs = 30
batch_size = 200
# Set's how much noise we're adding to the MNIST images
noise_factor = 0.5
sess.run(tf.global_variables_initializer())
for e in range(epochs):
    for ii in range(mnist.train.num_examples//batch_size):
        batch = mnist.train.next_batch(batch_size)
        # Get images from the batch
        imgs = batch[0].reshape((-1, 28, 28, 1))
        
        # Add random noise to the input images
        noisy_imgs = imgs + noise_factor * np.random.randn(*imgs.shape)
        # Clip the images to be between 0 and 1
        noisy_imgs = np.clip(noisy_imgs, 0., 1.)
        
        # Noisy images as inputs, original images as targets
        batch_cost, _ = sess.run([cost, opt], feed_dict={inputs_: noisy_imgs,
                                                         targets_: imgs})

        print("Epoch: {}/{}...".format(e+1, epochs),
              "Training loss: {:.4f}".format(batch_cost))









    



Epoch: 1/30... Training loss: 0.6962
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Epoch: 6/30... Training loss: 0.1203
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Epoch: 6/30... Training loss: 0.1177
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Epoch: 6/30... Training loss: 0.1181
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Epoch: 6/30... Training loss: 0.1189
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Epoch: 6/30... Training loss: 0.1189
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Epoch: 6/30... Training loss: 0.1166
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Epoch: 6/30... Training loss: 0.1187
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Epoch: 6/30... Training loss: 0.1199
Epoch: 6/30... Training loss: 0.1166
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Epoch: 11/30... Training loss: 0.1089
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Epoch: 29/30... Training loss: 0.1006
Epoch: 29/30... Training loss: 0.1029
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Epoch: 29/30... Training loss: 0.1016
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Epoch: 29/30... Training loss: 0.1008
Epoch: 29/30... Training loss: 0.1031
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Epoch: 29/30... Training loss: 0.1041
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Epoch: 29/30... Training loss: 0.1009
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Epoch: 29/30... Training loss: 0.1016
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Epoch: 29/30... Training loss: 0.1051
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Epoch: 29/30... Training loss: 0.1038
Epoch: 29/30... Training loss: 0.0992
Epoch: 29/30... Training loss: 0.1036
Epoch: 30/30... Training loss: 0.1039
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Epoch: 30/30... Training loss: 0.1041
Epoch: 30/30... Training loss: 0.1050
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Epoch: 30/30... Training loss: 0.1029
Epoch: 30/30... Training loss: 0.1055
Epoch: 30/30... Training loss: 0.1031
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Epoch: 30/30... Training loss: 0.1038
Epoch: 30/30... Training loss: 0.1031
Epoch: 30/30... Training loss: 0.0995
Epoch: 30/30... Training loss: 0.1010
Epoch: 30/30... Training loss: 0.1024
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Epoch: 30/30... Training loss: 0.1039
Epoch: 30/30... Training loss: 0.1047
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Epoch: 30/30... Training loss: 0.1052
Epoch: 30/30... Training loss: 0.1033
Epoch: 30/30... Training loss: 0.1023
Epoch: 30/30... Training loss: 0.1049
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Epoch: 30/30... Training loss: 0.1052
Epoch: 30/30... Training loss: 0.1005
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Epoch: 30/30... Training loss: 0.1038
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Epoch: 30/30... Training loss: 0.1043
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Epoch: 30/30... Training loss: 0.1046
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Epoch: 30/30... Training loss: 0.1031
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Epoch: 30/30... Training loss: 0.1010
Epoch: 30/30... Training loss: 0.1024
Epoch: 30/30... Training loss: 0.0985
Epoch: 30/30... Training loss: 0.1052
Epoch: 30/30... Training loss: 0.1031
Epoch: 30/30... Training loss: 0.1041
Epoch: 30/30... Training loss: 0.1059
Epoch: 30/30... Training loss: 0.1015
Epoch: 30/30... Training loss: 0.0995
Epoch: 30/30... Training loss: 0.1001
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Epoch: 30/30... Training loss: 0.1018
Epoch: 30/30... Training loss: 0.1024
Epoch: 30/30... Training loss: 0.1048
Epoch: 30/30... Training loss: 0.1026
Epoch: 30/30... Training loss: 0.1032
Epoch: 30/30... Training loss: 0.1010
Epoch: 30/30... Training loss: 0.1009
Epoch: 30/30... Training loss: 0.1027
Epoch: 30/30... Training loss: 0.1038
Epoch: 30/30... Training loss: 0.1050
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Epoch: 30/30... Training loss: 0.1031
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Epoch: 30/30... Training loss: 0.1021
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Epoch: 30/30... Training loss: 0.1018
Epoch: 30/30... Training loss: 0.1021
Epoch: 30/30... Training loss: 0.1038
Epoch: 30/30... Training loss: 0.1041
Epoch: 30/30... Training loss: 0.1014
Epoch: 30/30... Training loss: 0.1044
Epoch: 30/30... Training loss: 0.1060
Epoch: 30/30... Training loss: 0.1006
Epoch: 30/30... Training loss: 0.1022
Epoch: 30/30... Training loss: 0.1027
Epoch: 30/30... Training loss: 0.1024
Epoch: 30/30... Training loss: 0.1020
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Epoch: 30/30... Training loss: 0.1042
Epoch: 30/30... Training loss: 0.1010
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Epoch: 30/30... Training loss: 0.1049
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Epoch: 30/30... Training loss: 0.1029
Epoch: 30/30... Training loss: 0.1043
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Epoch: 30/30... Training loss: 0.1031
Epoch: 30/30... Training loss: 0.1029
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Epoch: 30/30... Training loss: 0.1042
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Epoch: 30/30... Training loss: 0.1003
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Epoch: 30/30... Training loss: 0.1008
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Epoch: 30/30... Training loss: 0.1040
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Epoch: 30/30... Training loss: 0.1038
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Epoch: 30/30... Training loss: 0.1031
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Epoch: 30/30... Training loss: 0.1026
Epoch: 30/30... Training loss: 0.0995
Epoch: 30/30... Training loss: 0.1043
Epoch: 30/30... Training loss: 0.1019
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Epoch: 30/30... Training loss: 0.1019
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Epoch: 30/30... Training loss: 0.1043
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Epoch: 30/30... Training loss: 0.1050
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Epoch: 30/30... Training loss: 0.1005
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Epoch: 30/30... Training loss: 0.1032
Epoch: 30/30... Training loss: 0.1004
Epoch: 30/30... Training loss: 0.1005
Epoch: 30/30... Training loss: 0.1039
Epoch: 30/30... Training loss: 0.1053
Epoch: 30/30... Training loss: 0.1022
Epoch: 30/30... Training loss: 0.1045
Epoch: 30/30... Training loss: 0.1016
Epoch: 30/30... Training loss: 0.0992
Epoch: 30/30... Training loss: 0.1021
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Epoch: 30/30... Training loss: 0.1019
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Epoch: 30/30... Training loss: 0.1001
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Epoch: 30/30... Training loss: 0.1046
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Epoch: 30/30... Training loss: 0.1086
Epoch: 30/30... Training loss: 0.1013
Epoch: 30/30... Training loss: 0.1044
Epoch: 30/30... Training loss: 0.0988
Epoch: 30/30... Training loss: 0.1049
Epoch: 30/30... Training loss: 0.1027
Epoch: 30/30... Training loss: 0.1010
Epoch: 30/30... Training loss: 0.1005
Epoch: 30/30... Training loss: 0.1041
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Epoch: 30/30... Training loss: 0.1037
Epoch: 30/30... Training loss: 0.1024
Epoch: 30/30... Training loss: 0.1051
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Epoch: 30/30... Training loss: 0.1016
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Epoch: 30/30... Training loss: 0.1031
Epoch: 30/30... Training loss: 0.1024
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Epoch: 30/30... Training loss: 0.1036
Epoch: 30/30... Training loss: 0.1047
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Epoch: 30/30... Training loss: 0.1031
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Epoch: 30/30... Training loss: 0.1041
Epoch: 30/30... Training loss: 0.1029
Epoch: 30/30... Training loss: 0.1027
Epoch: 30/30... Training loss: 0.1011
Epoch: 30/30... Training loss: 0.1045
Epoch: 30/30... Training loss: 0.1049
Epoch: 30/30... Training loss: 0.1019
Epoch: 30/30... Training loss: 0.1031
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Epoch: 30/30... Training loss: 0.1002
Epoch: 30/30... Training loss: 0.1027
Epoch: 30/30... Training loss: 0.1029
Epoch: 30/30... Training loss: 0.0986
Epoch: 30/30... Training loss: 0.1053
Epoch: 30/30... Training loss: 0.1011
Epoch: 30/30... Training loss: 0.1023
Epoch: 30/30... Training loss: 0.1037
Epoch: 30/30... Training loss: 0.1035
Epoch: 30/30... Training loss: 0.1025
Epoch: 30/30... Training loss: 0.1014
Epoch: 30/30... Training loss: 0.1019
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Epoch: 30/30... Training loss: 0.1040
Epoch: 30/30... Training loss: 0.1037
Epoch: 30/30... Training loss: 0.1047
Epoch: 30/30... Training loss: 0.1028
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Epoch: 30/30... Training loss: 0.1045
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Epoch: 30/30... Training loss: 0.1043
Epoch: 30/30... Training loss: 0.1031
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Epoch: 30/30... Training loss: 0.1029
Epoch: 30/30... Training loss: 0.1013
Epoch: 30/30... Training loss: 0.1019
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Epoch: 30/30... Training loss: 0.1033
Epoch: 30/30... Training loss: 0.1028
Epoch: 30/30... Training loss: 0.1031
Epoch: 30/30... Training loss: 0.1047
Epoch: 30/30... Training loss: 0.1029
Epoch: 30/30... Training loss: 0.1018
Epoch: 30/30... Training loss: 0.1015
Epoch: 30/30... Training loss: 0.0975
Epoch: 30/30... Training loss: 0.1003
Epoch: 30/30... Training loss: 0.1028
Epoch: 30/30... Training loss: 0.1023
Epoch: 30/30... Training loss: 0.1040
Epoch: 30/30... Training loss: 0.1047
Epoch: 30/30... Training loss: 0.1015
Epoch: 30/30... Training loss: 0.1044
Epoch: 30/30... Training loss: 0.1012
Epoch: 30/30... Training loss: 0.1007
Epoch: 30/30... Training loss: 0.1010
Epoch: 30/30... Training loss: 0.1051
Epoch: 30/30... Training loss: 0.1050
Epoch: 30/30... Training loss: 0.1027

Checking out the performance

Here I'm adding noise to the test images and passing them through the autoencoder. It does a suprisingly great job of removing the noise, even though it's sometimes difficult to tell what the original number is.



In [17]:

    
fig, axes = plt.subplots(nrows=2, ncols=10, sharex=True, sharey=True, figsize=(20,4))
in_imgs = mnist.test.images[:10]
noisy_imgs = in_imgs + noise_factor * np.random.randn(*in_imgs.shape)
noisy_imgs = np.clip(noisy_imgs, 0., 1.)

reconstructed = sess.run(decoded, feed_dict={inputs_: noisy_imgs.reshape((10, 28, 28, 1))})

for images, row in zip([noisy_imgs, reconstructed], axes):
    for img, ax in zip(images, row):
        ax.imshow(img.reshape((28, 28)), cmap='Greys_r')
        ax.get_xaxis().set_visible(False)
        ax.get_yaxis().set_visible(False)

fig.tight_layout(pad=0.1)