Book a Demo!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutPoliciesSign UpSign In
keras-team
GitHub Repository: keras-team/keras-io
 Path: blob/master/examples/vision/md/autoencoder.md
3508 views

Convolutional autoencoder for image denoising

Author: Santiago L. Valdarrama
 Date created: 2021/03/01
 Last modified: 2021/03/01
 Description: How to train a deep convolutional autoencoder for image denoising.

View in Colab • GitHub source

Introduction

This example demonstrates how to implement a deep convolutional autoencoder for image denoising, mapping noisy digits images from the MNIST dataset to clean digits images. This implementation is based on an original blog post titled Building Autoencoders in Keras by François Chollet.

Setup

import numpy as np
import matplotlib.pyplot as plt

from keras import layers
from keras.datasets import mnist
from keras.models import Model


def preprocess(array):
    """Normalizes the supplied array and reshapes it."""
    array = array.astype("float32") / 255.0
    array = np.reshape(array, (len(array), 28, 28, 1))
    return array


def noise(array):
    """Adds random noise to each image in the supplied array."""
    noise_factor = 0.4
    noisy_array = array + noise_factor * np.random.normal(
        loc=0.0, scale=1.0, size=array.shape
    )

    return np.clip(noisy_array, 0.0, 1.0)


def display(array1, array2):
    """Displays ten random images from each array."""
    n = 10
    indices = np.random.randint(len(array1), size=n)
    images1 = array1[indices, :]
    images2 = array2[indices, :]

    plt.figure(figsize=(20, 4))
    for i, (image1, image2) in enumerate(zip(images1, images2)):
        ax = plt.subplot(2, n, i + 1)
        plt.imshow(image1.reshape(28, 28))
        plt.gray()
        ax.get_xaxis().set_visible(False)
        ax.get_yaxis().set_visible(False)

        ax = plt.subplot(2, n, i + 1 + n)
        plt.imshow(image2.reshape(28, 28))
        plt.gray()
        ax.get_xaxis().set_visible(False)
        ax.get_yaxis().set_visible(False)

    plt.show()

Prepare the data

# Since we only need images from the dataset to encode and decode, we
# won't use the labels.
(train_data, _), (test_data, _) = mnist.load_data()

# Normalize and reshape the data
train_data = preprocess(train_data)
test_data = preprocess(test_data)

# Create a copy of the data with added noise
noisy_train_data = noise(train_data)
noisy_test_data = noise(test_data)

# Display the train data and a version of it with added noise
display(train_data, noisy_train_data)
``` Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11490434/11490434 ━━━━━━━━━━━━━━━━━━━━ 0s 0us/step
</div>
    
![png](/img/examples/vision/autoencoder/autoencoder_5_1.png)
    


---
## Build the autoencoder

We are going to use the Functional API to build our convolutional autoencoder.


```python
input = layers.Input(shape=(28, 28, 1))

# Encoder
x = layers.Conv2D(32, (3, 3), activation="relu", padding="same")(input)
x = layers.MaxPooling2D((2, 2), padding="same")(x)
x = layers.Conv2D(32, (3, 3), activation="relu", padding="same")(x)
x = layers.MaxPooling2D((2, 2), padding="same")(x)

# Decoder
x = layers.Conv2DTranspose(32, (3, 3), strides=2, activation="relu", padding="same")(x)
x = layers.Conv2DTranspose(32, (3, 3), strides=2, activation="relu", padding="same")(x)
x = layers.Conv2D(1, (3, 3), activation="sigmoid", padding="same")(x)

# Autoencoder
autoencoder = Model(input, x)
autoencoder.compile(optimizer="adam", loss="binary_crossentropy")
autoencoder.summary()

Model: "functional_1"

┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━┓
┃ Layer (type)                    ┃ Output Shape              ┃    Param # ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━┩
│ input_layer (InputLayer)        │ (None, 28, 28, 1)         │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d (Conv2D)                 │ (None, 28, 28, 32)        │        320 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ max_pooling2d (MaxPooling2D)    │ (None, 14, 14, 32)        │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d_1 (Conv2D)               │ (None, 14, 14, 32)        │      9,248 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ max_pooling2d_1 (MaxPooling2D)  │ (None, 7, 7, 32)          │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d_transpose                │ (None, 14, 14, 32)        │      9,248 │
│ (Conv2DTranspose)               │                           │            │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d_transpose_1              │ (None, 28, 28, 32)        │      9,248 │
│ (Conv2DTranspose)               │                           │            │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d_2 (Conv2D)               │ (None, 28, 28, 1)         │        289 │
└─────────────────────────────────┴───────────────────────────┴────────────┘

 Total params: 28,353 (110.75 KB)

 Trainable params: 28,353 (110.75 KB)

 Non-trainable params: 0 (0.00 B)

Now we can train our autoencoder using train_data as both our input data and target. Notice we are setting up the validation data using the same format.

autoencoder.fit(
    x=train_data,
    y=train_data,
    epochs=50,
    batch_size=128,
    shuffle=True,
    validation_data=(test_data, test_data),
)
``` Epoch 1/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 8s 9ms/step - loss: 0.2537 - val_loss: 0.0723 Epoch 2/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0718 - val_loss: 0.0691 Epoch 3/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0695 - val_loss: 0.0677 Epoch 4/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0682 - val_loss: 0.0669 Epoch 5/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0673 - val_loss: 0.0664 Epoch 6/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0668 - val_loss: 0.0660 Epoch 7/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0664 - val_loss: 0.0657 Epoch 8/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0661 - val_loss: 0.0654 Epoch 9/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0657 - val_loss: 0.0651 Epoch 10/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0655 - val_loss: 0.0648 Epoch 11/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0653 - val_loss: 0.0646 Epoch 12/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0651 - val_loss: 0.0644 Epoch 13/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0649 - val_loss: 0.0643 Epoch 14/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0647 - val_loss: 0.0641 Epoch 15/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0646 - val_loss: 0.0640 Epoch 16/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0645 - val_loss: 0.0639 Epoch 17/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0642 - val_loss: 0.0638 Epoch 18/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0641 - val_loss: 0.0638 Epoch 19/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0640 - val_loss: 0.0636 Epoch 20/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0639 - val_loss: 0.0637 Epoch 21/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0639 - val_loss: 0.0634 Epoch 22/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0637 - val_loss: 0.0634 Epoch 23/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0636 - val_loss: 0.0633 Epoch 24/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0637 - val_loss: 0.0632 Epoch 25/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0635 - val_loss: 0.0632 Epoch 26/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0635 - val_loss: 0.0631 Epoch 27/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0635 - val_loss: 0.0630 Epoch 28/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0635 - val_loss: 0.0629 Epoch 29/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0634 - val_loss: 0.0630 Epoch 30/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0633 - val_loss: 0.0629 Epoch 31/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0633 - val_loss: 0.0628 Epoch 32/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0632 - val_loss: 0.0628 Epoch 33/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0631 - val_loss: 0.0627 Epoch 34/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0631 - val_loss: 0.0627 Epoch 35/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0630 - val_loss: 0.0627 Epoch 36/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0631 - val_loss: 0.0626 Epoch 37/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0629 - val_loss: 0.0626 Epoch 38/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0630 - val_loss: 0.0627 Epoch 39/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0630 - val_loss: 0.0625 Epoch 40/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0629 - val_loss: 0.0625 Epoch 41/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0628 - val_loss: 0.0625 Epoch 42/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0629 - val_loss: 0.0625 Epoch 43/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0629 - val_loss: 0.0624 Epoch 44/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0628 - val_loss: 0.0624 Epoch 45/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0628 - val_loss: 0.0624 Epoch 46/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0627 - val_loss: 0.0625 Epoch 47/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0628 - val_loss: 0.0623 Epoch 48/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0627 - val_loss: 0.0623 Epoch 49/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0626 - val_loss: 0.0623 Epoch 50/50 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0626 - val_loss: 0.0622

<keras.src.callbacks.history.History at 0x7ff5889d9930>

</div>
Let's predict on our test dataset and display the original image together with
the prediction from our autoencoder.

Notice how the predictions are pretty close to the original images, although
not quite the same.


```python
predictions = autoencoder.predict(test_data)
display(test_data, predictions)
``` 313/313 ━━━━━━━━━━━━━━━━━━━━ 1s 1ms/step
</div>
    
![png](/img/examples/vision/autoencoder/autoencoder_11_1.png)
    


Now that we know that our autoencoder works, let's retrain it using the noisy
data as our input and the clean data as our target. We want our autoencoder to
learn how to denoise the images.


```python
autoencoder.fit(
    x=noisy_train_data,
    y=train_data,
    epochs=100,
    batch_size=128,
    shuffle=True,
    validation_data=(noisy_test_data, test_data),
)
``` Epoch 1/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.1110 - val_loss: 0.0922 Epoch 2/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0925 - val_loss: 0.0904 Epoch 3/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0910 - val_loss: 0.0895 Epoch 4/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0900 - val_loss: 0.0888 Epoch 5/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0892 - val_loss: 0.0882 Epoch 6/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0887 - val_loss: 0.0878 Epoch 7/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0884 - val_loss: 0.0874 Epoch 8/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0880 - val_loss: 0.0871 Epoch 9/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0876 - val_loss: 0.0869 Epoch 10/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0875 - val_loss: 0.0868 Epoch 11/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0872 - val_loss: 0.0864 Epoch 12/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0870 - val_loss: 0.0863 Epoch 13/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0869 - val_loss: 0.0860 Epoch 14/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0868 - val_loss: 0.0859 Epoch 15/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0865 - val_loss: 0.0857 Epoch 16/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0863 - val_loss: 0.0857 Epoch 17/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0863 - val_loss: 0.0858 Epoch 18/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0862 - val_loss: 0.0854 Epoch 19/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0859 - val_loss: 0.0856 Epoch 20/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0859 - val_loss: 0.0853 Epoch 21/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0858 - val_loss: 0.0851 Epoch 22/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0857 - val_loss: 0.0851 Epoch 23/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0856 - val_loss: 0.0850 Epoch 24/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0855 - val_loss: 0.0850 Epoch 25/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0853 - val_loss: 0.0849 Epoch 26/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0855 - val_loss: 0.0849 Epoch 27/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0853 - val_loss: 0.0849 Epoch 28/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0853 - val_loss: 0.0848 Epoch 29/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0853 - val_loss: 0.0850 Epoch 30/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0854 - val_loss: 0.0847 Epoch 31/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0851 - val_loss: 0.0846 Epoch 32/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0851 - val_loss: 0.0846 Epoch 33/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0849 - val_loss: 0.0846 Epoch 34/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0851 - val_loss: 0.0847 Epoch 35/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0849 - val_loss: 0.0846 Epoch 36/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0849 - val_loss: 0.0844 Epoch 37/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0849 - val_loss: 0.0845 Epoch 38/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0848 - val_loss: 0.0844 Epoch 39/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0849 - val_loss: 0.0843 Epoch 40/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0849 - val_loss: 0.0844 Epoch 41/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0848 - val_loss: 0.0844 Epoch 42/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0848 - val_loss: 0.0844 Epoch 43/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0849 - val_loss: 0.0846 Epoch 44/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0846 - val_loss: 0.0843 Epoch 45/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0847 - val_loss: 0.0845 Epoch 46/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0846 - val_loss: 0.0843 Epoch 47/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0845 - val_loss: 0.0842 Epoch 48/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0846 - val_loss: 0.0842 Epoch 49/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0847 - val_loss: 0.0846 Epoch 50/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0847 - val_loss: 0.0843 Epoch 51/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0846 - val_loss: 0.0842 Epoch 52/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0846 - val_loss: 0.0844 Epoch 53/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0844 - val_loss: 0.0842 Epoch 54/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0845 - val_loss: 0.0842 Epoch 55/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0845 - val_loss: 0.0841 Epoch 56/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0844 Epoch 57/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0845 - val_loss: 0.0841 Epoch 58/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0843 Epoch 59/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0842 Epoch 60/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0844 - val_loss: 0.0847 Epoch 61/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0846 - val_loss: 0.0840 Epoch 62/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0840 Epoch 63/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0841 Epoch 64/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0844 - val_loss: 0.0841 Epoch 65/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0841 Epoch 66/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0841 Epoch 67/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0840 Epoch 68/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0841 Epoch 69/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0840 Epoch 70/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0841 Epoch 71/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0844 - val_loss: 0.0841 Epoch 72/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0842 - val_loss: 0.0840 Epoch 73/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0841 Epoch 74/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0844 - val_loss: 0.0840 Epoch 75/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0842 - val_loss: 0.0840 Epoch 76/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0842 Epoch 77/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0842 - val_loss: 0.0841 Epoch 78/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0841 Epoch 79/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0840 Epoch 80/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0843 - val_loss: 0.0839 Epoch 81/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0842 - val_loss: 0.0842 Epoch 82/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0842 - val_loss: 0.0839 Epoch 83/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0841 - val_loss: 0.0840 Epoch 84/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0841 - val_loss: 0.0839 Epoch 85/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0841 - val_loss: 0.0839 Epoch 86/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0840 - val_loss: 0.0838 Epoch 87/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0841 - val_loss: 0.0839 Epoch 88/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0842 - val_loss: 0.0838 Epoch 89/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0842 - val_loss: 0.0838 Epoch 90/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0841 - val_loss: 0.0840 Epoch 91/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0841 - val_loss: 0.0839 Epoch 92/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0842 - val_loss: 0.0838 Epoch 93/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0841 - val_loss: 0.0838 Epoch 94/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0841 - val_loss: 0.0838 Epoch 95/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0840 - val_loss: 0.0837 Epoch 96/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0841 - val_loss: 0.0838 Epoch 97/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0841 - val_loss: 0.0838 Epoch 98/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0841 - val_loss: 0.0837 Epoch 99/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0841 - val_loss: 0.0838 Epoch 100/100 469/469 ━━━━━━━━━━━━━━━━━━━━ 2s 3ms/step - loss: 0.0839 - val_loss: 0.0839

<keras.src.callbacks.history.History at 0x7ff5889da230>

</div>
Let's now predict on the noisy data and display the results of our autoencoder.

Notice how the autoencoder does an amazing job at removing the noise from the
input images.


```python
predictions = autoencoder.predict(noisy_test_data)
display(noisy_test_data, predictions)
``` 313/313 ━━━━━━━━━━━━━━━━━━━━ 0s 523us/step
</div>
    
![png](/img/examples/vision/autoencoder/autoencoder_15_1.png)