{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learned Post-Processing for Computarized Tomography\n",
    "\n",
    "Computing the inverse of the Radon transform by means of the Filtered Back Projection (FBP) works well when the measurements where done for a high number of angles, however, this implies a lot of harmful radiation for the patients. Therefore the goal is to get good reconstructions with as few angles as possible.\n",
    "\n",
    "The learned post-processing is a great example of how we can use Deep Learning and Convolutional Neural Networks for such an Inverse Problem. The main idea is to first apply some pseudo-inverse, in this case the FBP, and then use a deep Neural Network that was trained with many samples to improve the results coming from the pseudo-inverse. If our forward operator is $A:X\\rightarrow Y$ and its pseudo inverse is $A^\\dagger: Y\\rightarrow X$ then\n",
    "\n",
    "$$x^\\delta = \\Lambda_\\theta (A^\\dagger y^\\delta)$$\n",
    "\n",
    "where $\\Lambda_\\theta: X \\rightarrow X$ is the network that makes the postprocessing.\n",
    "\n",
    "\n",
    "\n",
    "## Exercise 1\n",
    "\n",
    "**a)** Load the MNIST data set, in the same way it was done for the CNN example for classifying the digits, and create a data set consisting of pairs $(z_i, x_i)$ for training $\\Lambda_\\theta$, where $z_i=A^\\dagger y_i, y_i = Ax_i+ \\sigma \\eta$, $\\eta \\sim \\mathcal{N}(0,1)$, $A$ is the Radon transform operator and $A^\\dagger$ the FBP operator. Inistially set $\\sigma=10^{-2}$ but check what happens for different values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/python-3.5.5/lib/python3.5/site-packages/h5py-2.8.0-py3.5-linux-x86_64.egg/h5py/__init__.py:72: UserWarning: h5py is running against HDF5 1.10.2 when it was built against 1.8.16, this may cause problems\n",
      "  '{0}.{1}.{2}'.format(*version.hdf5_built_version_tuple)\n",
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7nzFjRhKL9jhnxceoaNfU1JTEWGG2koaBaP93VqiM3i/7HKPl/KzAHe1tz36W0TYObGxUTI9er5yyWcjdd7p7U+nrfQDWAhgDYCqABaVhCwBMq2oGIiJSFxVdVprZeQCuBLAcwCh331n6q1YAo+o6MxERqUjhPnQzGwJgIYCH3b2z+/8lcHc3M7rFmJnNBjC71omKiMjxFbpCN7P+OJbMX3P3N0rhNjMbXfr70QDa2WPdfa67T3D3CfWYsIiIcEW6XAzAywDWuvtz3f7qLQAzS1/PBMBPNBYRkV5R5JbLtQB+AeBzM1tVij0O4BkAfzaz+wFsBXBXz0yx77Cq/5QpU+hYVrWPlvW++OKLSaytra3C2cmJJFpGzrDOhmhpORsbbQnB4pMnT6Zjr7322iR2wQUX0LEtLS1J7L333qNj2ZYAUecJw7rFos+WHWYRdcSwf5/RvNh7iLpyWHcT2w4A4O8t6nKpZCuJ7somdHdfBiDqoflpVa8qIiJ1p5WiIiKZUEIXEcmEErqISCa0H/pxDBs2LImxfaQj27dvp/FHH3206jnJiWnHjh1JLCpsseJYtHUEO60+2h/80ksvTWJ33HEHHTt8eLr1UmtrKx27cePGJNbc3EzHtren3cus+MheHwAGDx6cxKKl9KxYGu3TzuYVFS8Ztk97FK9kOT/bkgCofisRXaGLiGRCCV1EJBNK6CIimVBCFxHJhBK6iEgm1OUiUgeVHLbADnzYu3cvHcuW80edEffff38SY0vTAWDXrl1JrLOzk479/PPPk1i0xJ51fbCDJNihGQDvUjlw4AAdyzpiRowYUdO8AN5FVEnXSdTlEr0eU8lWEt3pCl1EJBNK6CIimVBCFxHJhBK6iEgmVBQ9jnXr1iWxjz76iI6dOHFiT09HTmCs6Bbth8/ihw4domNZUfSmm26iY1mhMlo2v2XLliQWLf1nKtmve//+/UmMbasB8M8xKqCyQnQ0lhUkKyleRvvVswJqtHc6K2ZH2zhE8XJ0hS4ikgkldBGRTCihi4hkosgh0Y1mtsTM1phZs5k9VIr/2sy2m9mq0n/8xp6IiPSKInfejwB4xN2bzGwogM/MbFHp737n7r/puemJiEhRRQ6J3glgZ+nrfWa2FsCYnp7YiYBV/SdNmtQHM5ETHetgiDpXOjo6kli0vP2aa65JYrfddhsdO3bs2CTW1NRExy5cuDCJsUMgAH6oC3stABgyZEgSY1090VJ69vjocAnWCRItr2dzqGQpftS5Ugl2wEWkV7pczOw8AFcCWF4KPWBmfzWzeWbGjyAREZFeUTihm9kQAAsBPOzunQD+AOBCAONx7Ar+t8HjZpvZSjNbWYf5iohIoFBCN7P+OJbMX3P3NwDA3dvc/ai7fwfgjwCuZo9197nuPsHdJ9Rr0iIikirS5WIAXgaw1t2f6xYf3W3YbQBW1396IiJSVJE779cC+AWAz81sVSn2OIB7zGw8AAewBcAve2SGIicBVtRky/YBXmBrbGykY6dPn57EWOEQAJqbm5PYxx9/TMeuX7++8POygmJUxGWFYFYAjfZ/Z8XAqJjIxg4cOLDwvKKxLB5tKcC2D4gKqJXscV7J/uvdFelyWQaAfaJvV/WKIiLSI7RSVEQkE0roIiKZUEIXEcmEErqISCZ0wIVID+ns7KRxdrL9zTffTMeyk+27urro2G3btiWxTz/9lI5lHRdRl8ugQYOSWLQcv2jXR3S4REtLS6HXB/ghGdFBFGxrBhaLXq8eXS5Hjx4t/LxsbBG6QhcRyYQSuohIJpTQRUQyoYQuIpIJi27K98iLme0CsLX07QgAu3vtxXuP3lffGevuDX09CZG+0qsJ/XsvbLYyxx0Y9b5EpK/olouISCaU0EVEMtGXCX1uH752T9L7EpE+0Wf30EVEpL50y0VEJBO9ntDN7AYz+8LMNprZnN5+/Xoys3lm1m5mq7vFzjKzRWa2ofTn8L6cYzXMrNHMlpjZGjNrNrOHSvGT/r2J5KxXE7qZ9QPwIoAbAYzDsWPsxvXmHOrsFQA3/CA2B8Bid78YwOLS9yebIwAecfdxAP4FwL+Vfk45vDeRbPX2FfrVADa6+2Z3PwzgTwCm9vIc6sbdlwLo+EF4KoAFpa8XAJjWq5OqA3ff6e5Npa/3AVgLYAwyeG8iOevthD4GwN+6fd9SiuVklLvvLH3dCmBUX06mVmZ2HoArASxHZu9NJDcqivYgP9ZCdNK2EZnZEAALATzs7t/b3Ptkf28iOerthL4dQGO3739SiuWkzcxGA0Dpz/Y+nk9VzKw/jiXz19z9jVI4i/cmkqveTugrAFxsZueb2WkA7gbwVi/Poae9BWBm6euZAN7sw7lUxcwMwMsA1rr7c93+6qR/byI56/WFRWZ2E4D/BNAPwDx3/49enUAdmdnrACbj2E6EbQB+BeC/AfwZwD/h2M6Sd7n7DwunJzQzmwjg/wB8DuDv52k9jmP30U/q9yaSM60UFRHJhIqiIiKZUEIXEcmEErqISCaU0EVEMqGELiKSCSV0EZFMKKGLiGRCCV1EJBP/D+62XXanVSflAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import keras\n",
    "from keras.datasets import mnist\n",
    "import matplotlib.pyplot as plt\n",
    "from skimage.transform import iradon\n",
    "from skimage.transform import radon\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "angles = 5\n",
    "sigma = 1e-2\n",
    "theta = np.linspace(0., 180., angles, endpoint=False)\n",
    "\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n",
    "# Since we are not doing classification anymore we ignore the digit labels\n",
    "\n",
    "\n",
    "def generate_z(x):\n",
    "    z = []\n",
    "    for xi in x:\n",
    "        yi = radon(xi, theta=theta, circle=False)\n",
    "        yi_delta = yi + np.random.randn(*yi.shape) * sigma\n",
    "        zi = iradon(yi_delta, theta=theta, circle=False)\n",
    "        z += [zi]\n",
    "    return np.array(z)\n",
    "        \n",
    "\n",
    "z_train = generate_z(x_train)\n",
    "z_test = generate_z(x_test)\n",
    "\n",
    "\n",
    "for i in range(10):\n",
    "    plt.figure()\n",
    "    xi = x_train[y_train==i][0]\n",
    "    zi = z_train[y_train==i][0]\n",
    "\n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.imshow(xi, cmap='gray')\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.imshow(zi, cmap='gray')\n",
    "\n",
    "    plt.axis('off')\n",
    "        \n",
    "\n",
    "# data preparation (images should be 28 x 28 x 1 tensors)\n",
    "img_rows = 28\n",
    "img_cols = 28\n",
    "\n",
    "x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1)\n",
    "x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1)\n",
    "z_train = z_train.reshape(z_train.shape[0], img_rows, img_cols, 1)\n",
    "z_test = z_test.reshape(z_test.shape[0], img_rows, img_cols, 1)\n",
    "\n",
    "input_shape = (img_rows, img_cols, 1)\n",
    "\n",
    "# normalize images to have values between 0 and 1\n",
    "x_train = x_train.astype('float32')/255\n",
    "x_test = x_test.astype('float32')/255\n",
    "\n",
    "z_train = z_train.astype('float32')/255\n",
    "z_test = z_test.astype('float32')/255"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b)** Set $\\Lambda_\\theta$ to be a **U-Net** like neural network and train it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__________________________________________________________________________________________________\n",
      "Layer (type)                    Output Shape         Param #     Connected to                     \n",
      "==================================================================================================\n",
      "input_2 (InputLayer)            (None, 28, 28, 1)    0                                            \n",
      "__________________________________________________________________________________________________\n",
      "gaussian_noise_2 (GaussianNoise (None, 28, 28, 1)    0           input_2[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_12 (Conv2D)              (None, 14, 14, 16)   144         gaussian_noise_2[0][0]           \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_13 (BatchNo (None, 14, 14, 16)   64          conv2d_12[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "leaky_re_lu_11 (LeakyReLU)      (None, 14, 14, 16)   0           batch_normalization_13[0][0]     \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_13 (Conv2D)              (None, 14, 14, 16)   2304        leaky_re_lu_11[0][0]             \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_14 (BatchNo (None, 14, 14, 16)   64          conv2d_13[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "leaky_re_lu_12 (LeakyReLU)      (None, 14, 14, 16)   0           batch_normalization_14[0][0]     \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_14 (Conv2D)              (None, 7, 7, 32)     4608        leaky_re_lu_12[0][0]             \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_15 (BatchNo (None, 7, 7, 32)     128         conv2d_14[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "leaky_re_lu_13 (LeakyReLU)      (None, 7, 7, 32)     0           batch_normalization_15[0][0]     \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_15 (Conv2D)              (None, 7, 7, 32)     9216        leaky_re_lu_13[0][0]             \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_16 (BatchNo (None, 7, 7, 32)     128         conv2d_15[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "leaky_re_lu_14 (LeakyReLU)      (None, 7, 7, 32)     0           batch_normalization_16[0][0]     \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_16 (Conv2D)              (None, 7, 7, 2)      64          leaky_re_lu_14[0][0]             \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_17 (BatchNo (None, 7, 7, 2)      8           conv2d_16[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "leaky_re_lu_15 (LeakyReLU)      (None, 7, 7, 2)      0           batch_normalization_17[0][0]     \n",
      "__________________________________________________________________________________________________\n",
      "concatenate_3 (Concatenate)     (None, 7, 7, 34)     0           leaky_re_lu_14[0][0]             \n",
      "                                                                 leaky_re_lu_15[0][0]             \n",
      "__________________________________________________________________________________________________\n",
      "up_sampling2d_3 (UpSampling2D)  (None, 14, 14, 34)   0           concatenate_3[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_18 (BatchNo (None, 14, 14, 34)   136         up_sampling2d_3[0][0]            \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_17 (Conv2D)              (None, 14, 14, 32)   9792        batch_normalization_18[0][0]     \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_19 (BatchNo (None, 14, 14, 32)   128         conv2d_17[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "leaky_re_lu_16 (LeakyReLU)      (None, 14, 14, 32)   0           batch_normalization_19[0][0]     \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_19 (Conv2D)              (None, 14, 14, 2)    32          leaky_re_lu_12[0][0]             \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_18 (Conv2D)              (None, 14, 14, 32)   1024        leaky_re_lu_16[0][0]             \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_21 (BatchNo (None, 14, 14, 2)    8           conv2d_19[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_20 (BatchNo (None, 14, 14, 32)   128         conv2d_18[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "leaky_re_lu_18 (LeakyReLU)      (None, 14, 14, 2)    0           batch_normalization_21[0][0]     \n",
      "__________________________________________________________________________________________________\n",
      "concatenate_4 (Concatenate)     (None, 14, 14, 34)   0           batch_normalization_20[0][0]     \n",
      "                                                                 leaky_re_lu_18[0][0]             \n",
      "__________________________________________________________________________________________________\n",
      "up_sampling2d_4 (UpSampling2D)  (None, 28, 28, 34)   0           concatenate_4[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_22 (BatchNo (None, 28, 28, 34)   136         up_sampling2d_4[0][0]            \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_20 (Conv2D)              (None, 28, 28, 16)   4896        batch_normalization_22[0][0]     \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_23 (BatchNo (None, 28, 28, 16)   64          conv2d_20[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "leaky_re_lu_19 (LeakyReLU)      (None, 28, 28, 16)   0           batch_normalization_23[0][0]     \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_21 (Conv2D)              (None, 28, 28, 16)   256         leaky_re_lu_19[0][0]             \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_24 (BatchNo (None, 28, 28, 16)   64          conv2d_21[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_22 (Conv2D)              (None, 28, 28, 1)    17          batch_normalization_24[0][0]     \n",
      "==================================================================================================\n",
      "Total params: 33,409\n",
      "Trainable params: 32,881\n",
      "Non-trainable params: 528\n",
      "__________________________________________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "from keras.layers import Conv2D, GaussianNoise, LeakyReLU, Input, BatchNormalization, Concatenate, UpSampling2D\n",
    "from keras.models import Model\n",
    "\n",
    "def unet(input_shape,\n",
    "         noise=1.0/30,\n",
    "         num_output_channels=1,\n",
    "         num_channels_down=[16, 32],\n",
    "         num_channels_up=[16, 32],\n",
    "         num_channels_skip=[2, 2],\n",
    "         filter_size_down=[3, 3, 3],\n",
    "         filter_size_up=[3, 3, 3],\n",
    "         filter_skip_size=1,\n",
    "         act_fun=LeakyReLU,\n",
    "         need1x1_up=True,\n",
    "         need_bias=False):\n",
    "\n",
    "    n_scales = len(num_channels_down)\n",
    "    \n",
    "    down_layers = []\n",
    "\n",
    "    x = Input(shape=input_shape)\n",
    "    out = x\n",
    "    out = GaussianNoise(noise)(out)\n",
    "\n",
    "    for i in range(len(num_channels_down)):\n",
    "        out = Conv2D(filters=num_channels_down[i], kernel_size=filter_size_down[i], strides=(2, 2), use_bias=need_bias, padding='same')(out)\n",
    "        out = BatchNormalization()(out)\n",
    "        out = act_fun()(out)\n",
    "\n",
    "        out = Conv2D(num_channels_down[i], kernel_size=filter_size_down[i], use_bias=need_bias, padding='same')(out)\n",
    "        out = BatchNormalization()(out)\n",
    "        out = act_fun()(out)\n",
    "\n",
    "        down_layers += [out]\n",
    "\n",
    "    for i in range(len(num_channels_up)):\n",
    "        if num_channels_skip[-(i + 1)] != 0:\n",
    "            skip = Conv2D(num_channels_skip[-(i + 1)], filter_skip_size, use_bias=need_bias, padding='same')(down_layers[-(i + 1)])\n",
    "            skip = BatchNormalization()(skip)\n",
    "            skip = act_fun()(skip)\n",
    "            out = Concatenate()([out, skip])\n",
    "\n",
    "        out = UpSampling2D(size=(2, 2))(out)\n",
    "        out = BatchNormalization()(out)\n",
    "        out = Conv2D(num_channels_up[-(i+1)], filter_size_up[-(i+1)], use_bias=need_bias, padding='same')(out)\n",
    "        out = BatchNormalization()(out)\n",
    "        out = act_fun()(out)\n",
    "\n",
    "        if need1x1_up:\n",
    "            out = Conv2D(num_channels_up[-(i+1)], kernel_size=1, use_bias=need_bias, padding='same')(out)\n",
    "            out = BatchNormalization()(out)\n",
    "            act_fun()(out)\n",
    "\n",
    "    out = Conv2D(num_output_channels, kernel_size=1, activation='sigmoid', padding='same')(out)\n",
    "\n",
    "    model = Model(inputs=x, outputs=out)\n",
    "    return model\n",
    "\n",
    "\n",
    "model = unet(input_shape=input_shape)\n",
    "model.compile(loss='mse', optimizer='adam')\n",
    "\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/20\n",
      "60000/60000 [==============================] - 35s 577us/step - loss: 0.0150 - val_loss: 0.0081\n",
      "Epoch 2/20\n",
      "60000/60000 [==============================] - 31s 512us/step - loss: 0.0071 - val_loss: 0.0061\n",
      "Epoch 3/20\n",
      "60000/60000 [==============================] - 30s 505us/step - loss: 0.0063 - val_loss: 0.0058\n",
      "Epoch 4/20\n",
      "60000/60000 [==============================] - 31s 512us/step - loss: 0.0059 - val_loss: 0.0054\n",
      "Epoch 5/20\n",
      "60000/60000 [==============================] - 30s 504us/step - loss: 0.0056 - val_loss: 0.0051\n",
      "Epoch 6/20\n",
      "60000/60000 [==============================] - 31s 510us/step - loss: 0.0054 - val_loss: 0.0050\n",
      "Epoch 7/20\n",
      "60000/60000 [==============================] - 31s 510us/step - loss: 0.0053 - val_loss: 0.0049\n",
      "Epoch 8/20\n",
      "60000/60000 [==============================] - 31s 515us/step - loss: 0.0052 - val_loss: 0.0052\n",
      "Epoch 9/20\n",
      "60000/60000 [==============================] - 31s 514us/step - loss: 0.0051 - val_loss: 0.0049\n",
      "Epoch 10/20\n",
      "60000/60000 [==============================] - 31s 520us/step - loss: 0.0050 - val_loss: 0.0046\n",
      "Epoch 11/20\n",
      "60000/60000 [==============================] - 31s 515us/step - loss: 0.0050 - val_loss: 0.0048\n",
      "Epoch 12/20\n",
      "60000/60000 [==============================] - 31s 514us/step - loss: 0.0049 - val_loss: 0.0046\n",
      "Epoch 13/20\n",
      "60000/60000 [==============================] - 31s 517us/step - loss: 0.0049 - val_loss: 0.0047\n",
      "Epoch 14/20\n",
      "60000/60000 [==============================] - 31s 511us/step - loss: 0.0048 - val_loss: 0.0045\n",
      "Epoch 15/20\n",
      "60000/60000 [==============================] - 32s 527us/step - loss: 0.0048 - val_loss: 0.0044\n",
      "Epoch 16/20\n",
      "60000/60000 [==============================] - 33s 545us/step - loss: 0.0047 - val_loss: 0.0046\n",
      "Epoch 17/20\n",
      "60000/60000 [==============================] - 32s 538us/step - loss: 0.0047 - val_loss: 0.0047\n",
      "Epoch 18/20\n",
      "60000/60000 [==============================] - 32s 529us/step - loss: 0.0047 - val_loss: 0.0045\n",
      "Epoch 19/20\n",
      "60000/60000 [==============================] - 32s 527us/step - loss: 0.0046 - val_loss: 0.0043\n",
      "Epoch 20/20\n",
      "60000/60000 [==============================] - 32s 533us/step - loss: 0.0046 - val_loss: 0.0043\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x7feb7c10b240>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(z_train, x_train, validation_data=(z_test, x_test), epochs=20, verbose=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FBP (mean PSNR 11.99)\n",
      "Post-processing (mean PSNR 25.61)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skimage.measure import compare_psnr\n",
    "\n",
    "fbp_error = []\n",
    "pp_error = []\n",
    "for i in range(10):\n",
    "    xi = model.predict(np.array([z_test[i]]))\n",
    "    fbp_error += [compare_psnr(z_test[i][:,:,0], x_test[i][:,:,0], data_range=1)]\n",
    "    pp_error += [compare_psnr(xi[0,:,:,0], x_test[i][:,:,0], data_range=1)]\n",
    "    \n",
    "print('FBP (mean PSNR %.2f)' % np.mean(fbp_error))\n",
    "print('Post-processing (mean PSNR %.2f)' % np.mean(pp_error))\n",
    "    \n",
    "    \n",
    "for i in range(10):\n",
    "    plt.figure(figsize=(10,5))\n",
    "    xi = model.predict(np.array([z_test[i]]))\n",
    "\n",
    "    plt.subplot(1, 3, 1)\n",
    "    plt.imshow(z_test[i][:,:,0], cmap='gray')\n",
    "    plt.title('FBP (PSNR %.2f)' % compare_psnr(z_test[i][:,:,0], x_test[i][:,:,0], data_range=1))\n",
    "\n",
    "    plt.subplot(1, 3, 2)\n",
    "    plt.imshow(xi[0,:,:,0], cmap='gray')\n",
    "    plt.title('Post-Processing (PSNR %.2f)' % compare_psnr(xi[0,:,:,0], x_test[i][:,:,0], data_range=1))\n",
    "    plt.subplot(1, 3, 3)\n",
    "    plt.imshow(x_test[i][:,:,0], cmap='gray')\n",
    "    plt.title('Original')"
   ]
  }
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