week0_04 pictures_svd

.gitignore

@@ -110,3 +110,6 @@ venv.bak/
 *__solved*
 *__draft*
 testing/
+
+# IDEA
+.idea/

week0_04_svm_pca/week0_04_pictures_svd.ipynb

@@ -0,0 +1,254 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Pictures compression using SVD\n",
+    "In this exercise you are supposed to study how SVD could be used in image compression.\n",
+    "\n",
+    "_Based on open course in [Numerical Linear Algebra](https://github.com/oseledets/nla2018) by Ivan Oseledets_"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-03-19T19:53:33.168139Z",
+     "start_time": "2021-03-19T19:53:33.166488Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "# If you are using colab, uncomment this cell\n",
+    "\n",
+    "# ! wget https://raw.githubusercontent.com/girafe-ai/ml-mipt/a5bf18c/datasets/waiting.jpeg\n",
+    "# ! wget https://raw.githubusercontent.com/girafe-ai/ml-mipt/a5bf18c/datasets/mipt.jpg\n",
+    "# ! wget https://raw.githubusercontent.com/girafe-ai/ml-mipt/a5bf18c/datasets/simpsons.jpg\n",
+    "\n",
+    "# ! mkdir ../dataset\n",
+    "# ! mv -t ../dataset waiting.jpeg mipt.jpg simpsons.jpg"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-03-19T19:53:33.164791Z",
+     "start_time": "2021-03-19T19:53:32.704012Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "from PIL import Image"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 1. Singular values\n",
+    "\n",
+    "Compute the singular values of some predownloaded image (via the code provided below) and plot them. Do not forget to use logarithmic scale."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-03-19T19:53:33.268514Z",
+     "start_time": "2021-03-19T19:53:33.170197Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "face_raw = Image.open(\"../dataset/waiting.jpeg\")\n",
+    "face = np.array(face_raw).astype(np.uint8)\n",
+    "\n",
+    "plt.imshow(face_raw)\n",
+    "plt.xticks(())\n",
+    "plt.yticks(())\n",
+    "plt.title(\"Original Picture\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-03-19T19:53:33.272580Z",
+     "start_time": "2021-03-19T19:53:33.270472Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "# YOUR CODE HERE: Compute SVD and plot the singular values for different image channels"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 2. Compress\n",
+    "\n",
+    "Complete a function ```compress```, that performs SVD and truncates it (using $k$ singular values/vectors). See the prototype below. \n",
+    "\n",
+    "Note, that in case when your images are not grayscale you have to split your image to channels and work with matrices corresponding to different channels separately.\n",
+    "\n",
+    "Plot approximate reconstructed image $M_\\varepsilon$ of your favorite image such that $rank(M_\\varepsilon) = 5, 20, 50$ using ```plt.subplots```."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-03-19T19:53:33.276669Z",
+     "start_time": "2021-03-19T19:53:33.274057Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def compress(image: np.ndarray, k: int) -> (np.ndarray, np.ndarray):\n",
+    "    \"\"\"\n",
+    "    Perform svd decomposition and truncate it (using k singular values/vectors)\n",
+    "\n",
+    "    Parameters:\n",
+    "        image (np.array): input image (probably, colourful)\n",
+    "        k (int): approximation rank\n",
+    "\n",
+    "    Returns:\n",
+    "      reconst_matrix (np.array): reconstructed matrix (tensor in colourful case)\n",
+    "      s (np.array): array of singular values\n",
+    "    \"\"\"\n",
+    "    # YOUR CODE HERE: Compute per-channel SVD for and reconstruct the input image with the given approximation rank\n",
+    "    reconst_matrix = None\n",
+    "    s = None\n",
+    "\n",
+    "    return reconst_matrix, s"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 3. Discover\n",
+    "\n",
+    "Plot the following two figures for your favorite picture\n",
+    "* How relative error of approximation depends on the rank of approximation?\n",
+    "* How compression rate in terms of storing information ((singular vectors + singular numbers) / total size of image) depends on the rank of approximation?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-03-19T19:53:33.279835Z",
+     "start_time": "2021-03-19T19:53:33.278114Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "# YOUR CODE HERE"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 4. Compare\n",
+    "\n",
+    " Consider the following two pictures. Compute their approximations (with the same rank, or relative error). What do you see? Explain results."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-03-19T19:53:33.612398Z",
+     "start_time": "2021-03-19T19:53:33.281322Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "image_raw1 = Image.open(\"../dataset/mipt.jpg\")\n",
+    "image_raw2 = Image.open(\"../dataset/simpsons.jpg\")\n",
+    "\n",
+    "image1 = np.array(image_raw1).astype(np.uint8)\n",
+    "image2 = np.array(image_raw2).astype(np.uint8)\n",
+    "\n",
+    "plt.figure(figsize=(18, 6))\n",
+    "plt.subplot(1, 2, 1)\n",
+    "plt.imshow(image_raw1)\n",
+    "plt.title(\"One Picture\")\n",
+    "plt.xticks(())\n",
+    "plt.yticks(())\n",
+    "\n",
+    "plt.subplot(1, 2, 2)\n",
+    "plt.imshow(image_raw2)\n",
+    "plt.title(\"Another Picture\")\n",
+    "plt.xticks(())\n",
+    "plt.yticks(())\n",
+    "\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-03-19T19:53:33.617670Z",
+     "start_time": "2021-03-19T19:53:33.615929Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "# YOUR CODE HERE"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.11"
+  },
+  "toc": {
+   "base_numbering": 1,
+   "nav_menu": {},
+   "number_sections": true,
+   "sideBar": true,
+   "skip_h1_title": false,
+   "title_cell": "Table of Contents",
+   "title_sidebar": "Contents",
+   "toc_cell": false,
+   "toc_position": {},
+   "toc_section_display": true,
+   "toc_window_display": true
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}