diff --git a/solutions/week03/Projections and signal restoration.ipynb b/solutions/week03/Projections and signal restoration.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..f867fa5535cb1239f8f6fb5fc6ba71006e1d33cc --- /dev/null +++ b/solutions/week03/Projections and signal restoration.ipynb @@ -0,0 +1,1264 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "0b9af790", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [], + "source": [ + "# Initialize Otter\n", + "import otter\n", + "grader = otter.Notebook(\"Projections and signal restoration.ipynb\")" + ] + }, + { + "cell_type": "markdown", + "id": "4133723e-952b-4b1c-bb3d-a7f78a957024", + "metadata": {}, + "source": [ + "# Matrix Analysis 2025 - EE312\n", + "\n", + "## Week 3 - Signal restoration using projections\n", + "[LTS2](https://lts2.epfl.ch)" + ] + }, + { + "cell_type": "markdown", + "id": "fb42154f-8832-4960-9fee-3372b473ef69", + "metadata": {}, + "source": [ + "Let us consider a signal with $N$ elements, i.e. a vector in $\\mathbb{R}^N$. \n", + "Under our observations conditions, we can only recover partially the signal's values, the other remain unknown, i.e. we know that:\n", + "\n", + "$x[k] = x_k$ for $k\\in E = \\{e_0, e_1, \\dots,e_{M-1}\\}$, with $E\\in\\mathbb{N}^M$ and $e_i\\neq e_j \\forall i\\neq j$ (i.e. each known index is unique).\n", + "\n", + "We also make the assumption that the signal is contained within **lower frequencies of the spectrum**. This can be expressed using the (normalized) Fourier matrix you have constructed last week $\\hat{W}$.\n", + "\n", + "In this notebook, we will try to reconstruct the signal by projecting its observation successively on the Fourier subspace defined above, then back to its original domain (with the constraint regarding its values), then on the Fourier domain, etc. This is a simplified version of a more general method called [\"Projection onto convex sets\" (POCS)](https://en.wikipedia.org/wiki/Projections_onto_convex_sets). The method is illustrated by the figure below (of course you do not project on lines but on spaces having larger dimension).\n", + "\n", + "\n", + "\n", + "### 1. Low-pass filter\n", + "Let us first create example signals to validate our implementation of the filtering operation." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "d238cbc9-055f-4d55-a6ae-29d83881e2f5", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "N = 100\n", + "k = np.arange(0, N)\n", + "w1 = 3\n", + "w2 = 7\n", + "w3 = 12\n", + "\n", + "# generate simple signals\n", + "x1 = np.cos(2*w1*np.pi*k/N) + np.sin(2*w2*np.pi*k/N)\n", + "x2 = np.sin(2*w1*np.pi*k/N) + np.cos(2*w3*np.pi*k/N)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "59a703e8-f351-4a02-8278-12560a67b023", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[<matplotlib.lines.Line2D at 0x10f60da10>]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# visualize the base signals\n", + "plt.plot(x1)\n", + "plt.plot(x2, 'r')" + ] + }, + { + "cell_type": "markdown", + "id": "09249ca9-e441-4537-9bc5-018be67bc099", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "1. Implement a function that returns the normalized Fourier matrix of size N (use your implementation from week 2)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "f886d8a6-4cb7-4187-ae4b-4615a06caa2d", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "outputs": [], + "source": [ + "def fourier_matrix(N):\n", + " # BEGIN SOLUTION\n", + " if N <= 0:\n", + " raise ValueError(\"Invalid size\")\n", + " k = np.arange(0, N)\n", + " Ws = np.exp(-2j*np.pi*np.outer(k, k)/N)\n", + " return Ws/np.sqrt(N)\n", + " # END SOLUTION" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f367f4e1", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [], + "source": [ + "grader.check(\"q1\")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "62fae5a8-f3c4-477b-a53f-a0106730b842", + "metadata": {}, + "outputs": [], + "source": [ + "W_hat = fourier_matrix(N)" + ] + }, + { + "cell_type": "markdown", + "id": "1e0a2337-446d-49d3-8521-55d07a1539bc", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "Let $X = \\hat{W}x$, $X$ is the *discrete Fourier transform* of the input signal $x$. The frequency condition can then be rewritten as \n", + "\n", + "$X[k] = 0$ for $w_c < k\\leq N-w_c$. \n", + "\n", + "2. Implement the function that returns a $N\\times N$ matrix $P$, s.t. $PX$ satisfies the above condition for a given $w_c$. Make sure the input values are valid, if not raise a `ValueError` exception." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "aeed4067-1130-4e6c-9fbd-ab8d0a3a41c0", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "outputs": [], + "source": [ + "def lowpass_matrix(N, w_c):\n", + " \"\"\"\n", + " Computes the P matrix that will remove high-frequency coefficients in a DFT transformed signal\n", + "\n", + " Parameters\n", + " ----------\n", + " N : length of the input signal\n", + " w_c : cutoff frequency\n", + "\n", + " Returns\n", + " -------\n", + " The P matrix\n", + " \"\"\"\n", + " # BEGIN SOLUTION\n", + " if N < 1:\n", + " raise ValueError(\"Invalid input size\")\n", + " if w_c < 0 or w_c > N//2:\n", + " raise ValueError(\"Invalid w_c supplied\")\n", + " P = np.eye(N)\n", + " P[w_c:N - w_c + 1, w_c:N - w_c + 1] = 0 # be careful with indices, otherwise you end up with a non-real filtered output\n", + " return P\n", + " # END SOLUTION" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "38529611", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [], + "source": [ + "grader.check(\"q2\")" + ] + }, + { + "cell_type": "markdown", + "id": "fef68750-d97f-4625-bd5e-5f13e7894f7d", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "3. Now let us try the filtering on the test signals and make sure it behaves appropriately. Using the matrix $P$ defined above, choose the parameter $w_c$ approiately s.t. the filtered signals retain $w_1$ and $w_2$ but discard $w_3$." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "bc1370d5-c7b2-4598-b573-d57bec56aa1b", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "outputs": [], + "source": [ + "w_c = 10 # SOLUTION" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "85787e70-1427-4860-8a7b-94d20432bd76", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "outputs": [], + "source": [ + "# Compute the DFT of x1 and x2\n", + "X1 = W_hat@x1\n", + "X2 = W_hat@x2\n", + "\n", + "# Get the lowpass filter matrix\n", + "P = lowpass_matrix(N, w_c)\n", + "\n", + "# Filter X1 and X2 and apply inverse DFT\n", + "x1_f = np.real(np.conj(W_hat.T)@P@X1) # SOLUTION\n", + "x2_f = np.real(np.conj(W_hat.T)@P@X2) # SOLUTION" + ] + }, + { + "cell_type": "markdown", + "id": "700eb2e2-3137-4916-a829-9e8e2ba8c6e5", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "NB: Make sure the filtered output is **real** (or its imaginary part should be smaller than $10^{-12}$)." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "e960728d-c2c0-4b9d-ab73-3db971f559a1", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[<matplotlib.lines.Line2D at 0x11f158d10>]" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the filtered signals\n", + "# x1_f should still contain both frequencies, x2_f only one\n", + "plt.plot(x1_f)\n", + "plt.plot(x2_f, 'r')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b6f5b443", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [], + "source": [ + "grader.check(\"q3\")" + ] + }, + { + "cell_type": "markdown", + "id": "c34b8fc7-8a51-4fe5-a6ab-1cc27da2cd1e", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "<!-- BEGIN QUESTION -->\n", + "\n", + "4. Prove that $P$ is a projection." + ] + }, + { + "cell_type": "markdown", + "id": "0cd9f0a9", + "metadata": { + "tags": [ + "otter_answer_cell" + ] + }, + "source": [ + "_Type your answer here, replacing this text._" + ] + }, + { + "cell_type": "markdown", + "id": "d4762468-a1dc-40c6-a5ca-be00c3f945de", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "source": [ + "$P$ is a projection, since $P^2=P$ (any diagonal matrix with only 0s and 1s on its diagonal would satisfy this)" + ] + }, + { + "cell_type": "markdown", + "id": "7f17f3ae-6a39-4e86-a29c-879c96b4e5fb", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "<!-- END QUESTION -->\n", + "\n", + "### 2. Signal extension\n", + "\n", + "In order to express the condition on $x[k]$ as a pure matrix operation we need to make use of an extension of the input signal and design a slightly different Fourier transform matrix to use properly those extended signals. \n", + "\n", + "Let us denote by $x_E$ the vector from $\\mathbb{R}^M$ containing the known values of $x$, i.e. the $x_k$ for $k\\in E$.\n", + "\n", + "For each vector $y$ in $\\mathbb{R}^N$ we define its extension as $\\tilde{y} = \\begin{pmatrix}y \\\\ x_E\\end{pmatrix}$. \n", + "\n", + "**This notation will remain throughout the notebook**, i.e. a vector with a tilde denotes its extension made by adding the $x_E$ values at the end." + ] + }, + { + "cell_type": "markdown", + "id": "f9434f5f-ceb9-42bf-9b5e-bd7d7a94dae8", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "5. Let us define the matrix $B_E$ and $y=B_E x$, s.t. $y[k] = 0$ if $k\\in E$ and $y[k] = x[k]$ otherwise. Write a function that returns its extended version $\\tilde{B_E}$ s.t. $\\tilde{y}=\\tilde{B_E}\\tilde{x}$, for any $x\\in\\mathbb{R}^N$. \n", + "\n", + "- $\\tilde{B_E}$ is a square matrix of size $N+M$.\n", + "- Check the validity of parameters and raise a `ValueError` in case of invalid inputs." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "dae1c4aa-c6ce-4f35-b309-aa6dd09e9abf", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "outputs": [], + "source": [ + "def Bt_E(N, E):\n", + " \"\"\"\n", + " Computes the $\\tilde{B}_E$ matrix \n", + "\n", + " Parameters\n", + " ----------\n", + " N : length of the input signal\n", + " E : list of suitable indices. e.g. for N=5 a valid E could be [1, 3]\n", + "\n", + " Returns\n", + " -------\n", + " The $\\tilde{B}_E$ matrix \n", + " \"\"\"\n", + " # BEGIN SOLUTION\n", + " E = np.unique(E) # remove the duplicates from E\n", + " M = len(E)\n", + " if not np.all(np.array(E)<N):\n", + " raise ValueError(\"Invalid list of indices supplied\")\n", + " if not np.all(np.array(E)>=0):\n", + " raise ValueError(\"Negative indices supplied\")\n", + " if N<1 or M >= N:\n", + " raise ValueError(\"Invalid dimensions\")\n", + " \n", + " B = np.eye((N + M))\n", + "\n", + " # coefficients on the diagonal having indices in E should be zeroed\n", + " for p in zip(E, E):\n", + " B[p] = 0.\n", + " return B\n", + " # END SOLUTION" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "751ff499", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [], + "source": [ + "grader.check(\"q5\")" + ] + }, + { + "cell_type": "markdown", + "id": "853c1a3b-9ed9-461c-86f9-12992e07337d", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "Let us know design $C_E$ as an operator from $\\mathbb{R}^{N+M} \\rightarrow \\mathbb{R}^{N+M}$ such that when applied to any extended vector $\\tilde{z}$ s.t. $\\tilde{z}[k] = 0, \\forall k\\in E$ as input (i.e. for instance the output of $\\tilde{B}_E$), it generates a vector $\\tilde{z}_R$ s.t.:\n", + "\n", + "$\\tilde{z}_R[k] = \\left\\{\\begin{matrix} x_k \\mbox{Â if } k\\in E \\\\ \\tilde{z}[k] \\mbox{ otherwise} \\end{matrix}\\right.$\n", + "\n", + "6. Write a function that generates $C_E$. " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "932ae153-f336-4b0f-b7c0-774c02ccaad1", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "outputs": [], + "source": [ + "def C_E(N, E):\n", + " \"\"\"\n", + " Computes the $C_E$ matrix \n", + "\n", + " Parameters\n", + " ----------\n", + " N : length of the input signal\n", + " E : list of suitable indices. e.g. for N=5 a valid E could be [1, 3]\n", + "\n", + " Returns\n", + " -------\n", + " The $C_E$ matrix \n", + " \"\"\"\n", + " # BEGIN SOLUTION\n", + " E = np.unique(E) # remove the duplicates from E\n", + " M = len(E)\n", + " if not np.all(np.array(E)<N):\n", + " raise ValueError(\"Invalid list of indices supplied\")\n", + " if not np.all(np.array(E)>=0):\n", + " raise ValueError(\"Negative indices supplied\")\n", + " if N<1 or M >= N:\n", + " raise ValueError(\"Invalid dimensions\")\n", + " \n", + " C = np.eye(N+M)\n", + " for p in zip(range(M), E):\n", + " C[p[1], N+p[0]] = 1.\n", + " return C\n", + " # END SOLUTION" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "473d2fb2", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [], + "source": [ + "grader.check(\"q6\")" + ] + }, + { + "cell_type": "markdown", + "id": "0e57be3f-1c44-445a-86ad-07e20fbcd1d2", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "<!-- BEGIN QUESTION -->\n", + "\n", + "7. What is the effect of $D_E = C_E \\tilde{B}_E$ on an extended signal $\\tilde{x}$ ? " + ] + }, + { + "cell_type": "markdown", + "id": "786cd4ed", + "metadata": { + "tags": [ + "otter_answer_cell" + ] + }, + "source": [ + "_Type your answer here, replacing this text._" + ] + }, + { + "cell_type": "markdown", + "id": "0a3fc7c9-f00f-4eae-aa7d-182c9800d3b9", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "source": [ + "The effect of $D_E$ is to replace values by the known initial values." + ] + }, + { + "cell_type": "markdown", + "id": "3b2caf03-41cb-41f9-93eb-778047b9b944", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "<!-- END QUESTION -->\n", + "\n", + "<!-- BEGIN QUESTION -->\n", + "\n", + "8. Verify (numerically on an example) that $D_E$ is a projector. You can use the function `numpy.testing.assert_array_almost_equal` to check that arrays are almost equal (with a good precision)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "94dbc7f8-c2fc-4337-9828-dd2e3311830d", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "outputs": [], + "source": [ + "# Set some parameters\n", + "N=5\n", + "E=[1,3]\n", + "# Compute D_E\n", + "D_E = C_E(N, E)@Bt_E(N, E) # SOLUTION\n", + "# Now check that D_E is a projector\n", + "# BEGIN SOLUTION\n", + "np.testing.assert_array_almost_equal(D_E@D_E - D_E, np.zeros(D_E.shape))\n", + "# END SOLUTION" + ] + }, + { + "cell_type": "markdown", + "id": "7fb30993-5350-4e9b-aa45-b657b450a3a1", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "<!-- END QUESTION -->\n", + "\n", + "### 3. Extended signals in the Fourier domain\n", + "Let us now define an operator that will work almost as the normalized Fourier transform, except that it will be applied to the extended signals and preserve the $x_E$ part. This can be easily done using the following block matrix:\n", + "\n", + "$\\tilde{W} = \\begin{pmatrix}\\hat{W} & 0 \\\\0 & I_M\\end{pmatrix}$.\n", + "\n", + "\n", + "Using this definition, multiplying an extended signal $\\tilde{x}$ by $\\tilde{W}$ will result in a vector containing the Fourier transform of $x$ followed by $x_E$, preserving the known initial values." + ] + }, + { + "cell_type": "markdown", + "id": "3157e22e-f7d7-44b8-a4fd-9ddec1d7aa8a", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "<!-- BEGIN QUESTION -->\n", + "\n", + "9. Prove that $\\tilde{W}$ is orthonormal. " + ] + }, + { + "cell_type": "markdown", + "id": "7abf655c", + "metadata": { + "tags": [ + "otter_answer_cell" + ] + }, + "source": [ + "_Type your answer here, replacing this text._" + ] + }, + { + "cell_type": "markdown", + "id": "3bf8cf4c-4055-48b3-937a-b5f48d5223eb", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "source": [ + "$\\tilde{W}$ is orthonormal: it is block-diagonal and each block is orthonormal. It is then fairly easy to check that $\\tilde{W}\\tilde{W}^H=I$. " + ] + }, + { + "cell_type": "markdown", + "id": "f140c720-eaed-4fd2-8b9f-6b99a1a5b0ff", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "<!-- END QUESTION -->\n", + "\n", + "10. Write a function that returns $\\tilde{W}$." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "b744a698-40d5-41a6-9623-76a19f50bcd2", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "outputs": [], + "source": [ + "def Wt_E(N, E):\n", + " \"\"\"\n", + " Computes the $\\tilde{W}_E$ matrix \n", + "\n", + " Parameters\n", + " ----------\n", + " N : length of the input signal\n", + " E : list of suitable indices. e.g. for N=5 a valid E could be [1, 3]\n", + "\n", + " Returns\n", + " -------\n", + " The $\\tilde{W}_E$ matrix \n", + " \"\"\"\n", + " # BEGIN SOLUTION\n", + " E = np.unique(E) # remove the duplicates from E\n", + " M = len(E)\n", + " if not np.all(np.array(E)<N):\n", + " raise ValueError(\"Invalid list of indices supplied\")\n", + " if not np.all(np.array(E)>=0):\n", + " raise ValueError(\"Negative indices supplied\")\n", + " if N<1 or M >= N:\n", + " raise ValueError(\"Invalid dimensions\")\n", + " \n", + " W_hat = fourier_matrix(N)\n", + " W_tilde = np.zeros((N+M, N+M), dtype=complex)\n", + " W_tilde[:N, :N] = W_hat\n", + " W_tilde[N:, N:] = np.eye(M)\n", + " return W_tilde\n", + " # END SOLUTION" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "60244622", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [], + "source": [ + "grader.check(\"q10\")" + ] + }, + { + "cell_type": "markdown", + "id": "1afee45d-78e6-498b-905b-cbc97eeaf2d5", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "11. Recalling the low-pass matrix $P$ defined previously, build $\\tilde{P}$ s.t. when applied to $\\tilde{W}\\tilde{x}$ it results in a vector containing the filtered values (still in the Fourier domain) followed by $x_E$." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "4576bfbc-a249-4d89-919d-47763c8a60f9", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "outputs": [], + "source": [ + "def Pt_E(N, M, w_c):\n", + " # BEGIN SOLUTION\n", + " P = np.eye(N+M) # initialize with an all-pass filter\n", + " P[:N, :N] = lowpass_matrix(N, w_c)\n", + " return P\n", + " # END SOLUTION" + ] + }, + { + "cell_type": "markdown", + "id": "781d7752-74ae-4ec2-8ea2-4279b54ee5e7", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "<!-- BEGIN QUESTION -->\n", + "\n", + "12. A signal $\\tilde{x}$ will be filtered by doing $\\tilde{W}^H \\tilde{P}\\tilde{W}\\tilde{x}$.\n", + "Prove that this is a projection." + ] + }, + { + "cell_type": "markdown", + "id": "d38cefa0", + "metadata": { + "tags": [ + "otter_answer_cell" + ] + }, + "source": [ + "_Type your answer here, replacing this text._" + ] + }, + { + "cell_type": "markdown", + "id": "041ea2c5-226e-4e71-8109-61c942f8fde9", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "source": [ + "$\\tilde{W}^H \\tilde{P}\\tilde{W}$ is a projection since\n", + "\n", + "$\\tilde{W}^H \\tilde{P}\\tilde{W}\\tilde{W}^H \\tilde{P}\\tilde{W} = \\tilde{W}^H \\tilde{P}\\tilde{P}\\tilde{W}$ (grouping the middle term $\\tilde{W}\\tilde{W}^H=I$)\n", + "\n", + "Since $\\tilde{P}$ is a projection, this is equal to $\\tilde{W}^H \\tilde{P}\\tilde{W}$.\n" + ] + }, + { + "cell_type": "markdown", + "id": "1c8c4469-7264-4968-b700-897be635a193", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "<!-- END QUESTION -->\n", + "\n", + "### 4. Signal restoration" + ] + }, + { + "cell_type": "markdown", + "id": "ac24806d-105d-4fbf-bc98-788dbcc7c0ba", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "<!-- BEGIN QUESTION -->\n", + "\n", + "13. We can now use all defined above to implement a function that performs an iteration, taking as input the extension of $x$ as defined above, that does the following:\n", + "- compute the filtered version of the signal using $\\tilde{W}^H \\tilde{P}\\tilde{W}$ (i.e. projecting on the space of \"smooth signals\")\n", + "- restore the known values in the signal by using $D_E = C_E\\tilde{B}_E$ (i.e project back on the space of signals having the known initial values we have set)\n", + "\n", + "Make sure to force the result to real values by using `np.real` before returning" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "155e3277-bcef-44ed-b53f-a1b2e5ad7363", + "metadata": { + "tags": [ + "otter_assign_solution_cell" + ] + }, + "outputs": [], + "source": [ + "def restoration_iter(Wt, Pt, Dt, xt):\n", + " \"\"\"\n", + " Performs a full restoration iteration by\n", + " - projecting the signal into Fourier, performing low-pass filtering followed by inverse DFT\n", + " - restoring the known initial values into the filtered signal\n", + "\n", + " Parameters\n", + " ----------\n", + " Wt : \\tilde{W} matrix\n", + " Pt : \\tilde{P} matrix\n", + " Dt : \\tilde{D} matrix\n", + " xt : \\tilde{x} vector\n", + "\n", + " Returns\n", + " -------\n", + " The new $\\tilde{x} vector after the iteration\n", + " \"\"\"\n", + " # BEGIN SOLUTION\n", + " # project in fourier\n", + " X = Wt@xt\n", + " # filter and inverse DFT\n", + " z = np.conjugate(Wt.T)@(Pt@X)\n", + " \n", + " # restore known values\n", + " xr = Dt@z\n", + " return np.real(xr)\n", + " # END SOLUTION" + ] + }, + { + "cell_type": "markdown", + "id": "758aa9ce-1ebc-49e1-b2f6-ca8e1035b31c", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "<!-- END QUESTION -->\n", + "\n", + "<!-- BEGIN QUESTION -->\n", + "\n", + "15. Finally we are ready to apply all this to an example." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "b467649e-2a46-40f2-bc98-73c354fb0484", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [], + "source": [ + "# Setup an example\n", + "N = 100\n", + "w_c = 10 # cut-off\n", + "w1 = 3\n", + "w2 = 7\n", + "E = np.array([0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95])\n", + "# E = np.array([0, 10, 20, 30, 40, 50, 60, 70, 80, 90]) # try with less known points\n", + "M = len(E)\n", + "x = np.cos(2*w1*np.pi*np.arange(0, N)/N) + np.sin(2*w2*np.pi*np.arange(0,N)/N) # original signal\n", + "\n", + "# Create a signal that is only noise, except at known initial values\n", + "y = np.random.rand(N) # \n", + "y[E] = x[E] # restore known values\n", + "xe = x[E]" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "510b6f8f-b1c2-48b7-af00-eee8e55b5868", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[<matplotlib.lines.Line2D at 0x11f202650>]" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(y) # plot the \"acquired\" signal\n", + "plt.plot(x, 'r+-', alpha=0.5) # plot the ground truth signal" + ] + }, + { + "cell_type": "markdown", + "id": "b71f1ff5-73d6-4bc1-ba06-1452c8bf8adb", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "Generate $\\tilde{y}$ (this only need to be done once)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "4e0943bf-0f35-4837-b6db-1615ba466ae5", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [], + "source": [ + "yt = np.append(y, xe) # SOLUTION" + ] + }, + { + "cell_type": "markdown", + "id": "c25239d9-3015-4a33-b0c0-0c906ee4129e", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "Run a number of iterations of the method and plot the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "6aaf1a71-6c2a-4f43-a51e-82b40cc6d6d0", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [], + "source": [ + "def signal_restore(Wt, Pt, Dt, yt, niter=20):\n", + " yr0 = yt # initialize\n", + " for k in range(niter):\n", + " yr1 = restoration_iter(Wt, Pt, Dt, yr0)\n", + " yr0 = yr1\n", + " return yr1" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "951418c2-ee12-4e8d-8f58-cba29d26dd7e", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [], + "source": [ + "Wt = Wt_E(N, E)\n", + "Dt = C_E(N, E)@Bt_E(N, E)\n", + "Pt = Pt_E(N, M, w_c)\n", + "yr = signal_restore(Wt, Pt, Dt, yt)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "43b3d939-eeb2-4171-9293-0076f1c06c83", + "metadata": { + "deletable": false, + "editable": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[<matplotlib.lines.Line2D at 0x11f29d390>]" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(yr[:N]) # plot reconstructed signal\n", + "plt.plot(x, 'r+', alpha=0.7) # plot original for comparison" + ] + }, + { + "cell_type": "markdown", + "id": "bf876405-b60c-4f7c-9162-56d58cafd19f", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "Depending on $M$, you will find that the method can reconstruct perfectly the signal or not. " + ] + }, + { + "cell_type": "markdown", + "id": "ccf83efe", + "metadata": { + "deletable": false, + "editable": false + }, + "source": [ + "<!-- END QUESTION -->\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.11.10" + }, + "otter": { + "OK_FORMAT": true, + "tests": { + "q1": { + "name": "q1", + "points": null, + "suites": [ + { + "cases": [ + { + "code": ">>> from scipy.linalg import dft\n>>> np.testing.assert_array_almost_equal(fourier_matrix(16), dft(16, scale='sqrtn'))\n", + "failure_message": "Check your implementation", + "hidden": false, + "locked": false, + "success_message": "Good, your implementation returns correct results" + }, + { + "code": ">>> W = fourier_matrix(8)\n>>> np.testing.assert_array_almost_equal(np.conj(W.T) @ W, np.eye(8))\n", + "failure_message": "Check your implementation, resulting matrix should be orthogonal.", + "hidden": false, + "locked": false, + "success_message": "Good, your implementation returns an orthogonal matrix" + } + ], + "scored": true, + "setup": "", + "teardown": "", + "type": "doctest" + } + ] + }, + "q10": { + "name": "q10", + "points": null, + "suites": [ + { + "cases": [ + { + "code": ">>> from scipy.linalg import dft\n>>> w = Wt_E(12, [1, 2, 4])\n>>> assert w.shape == (15, 15)\n>>> np.testing.assert_array_almost_equal(w[:12, :12], dft(12, scale='sqrtn'))\n>>> np.testing.assert_array_almost_equal(w[12:, 12:], np.eye(3))\n", + "failure_message": "Check your implementation", + "hidden": false, + "locked": false, + "success_message": "Good, your implementation returns correct results" + }, + { + "code": ">>> with np.testing.assert_raises(ValueError):\n... Wt_E(10, [12, 5])\n>>> with np.testing.assert_raises(ValueError):\n... Wt_E(8, [2, -1])\n>>> with np.testing.assert_raises(ValueError):\n... Wt_E(5, [1, 2, 3, 4, 5])\n>>> with np.testing.assert_raises(ValueError):\n... Wt_E(0, [])\n", + "failure_message": "Did you forget to validate the input parameters before performing the computation ?", + "hidden": false, + "locked": false, + "success_message": "Good, you properly validated parameters before computing the result" + } + ], + "scored": true, + "setup": "", + "teardown": "", + "type": "doctest" + } + ] + }, + "q2": { + "name": "q2", + "points": null, + "suites": [ + { + "cases": [ + { + "code": ">>> np.testing.assert_array_almost_equal(lowpass_matrix(20, 0), np.zeros((20, 20)))\n>>> B = np.eye(16)\n>>> B[8:9, 8:9] = 0\n>>> np.testing.assert_array_almost_equal(lowpass_matrix(16, 8), B)\n>>> B[4:13, 4:13] = 0\n>>> np.testing.assert_array_almost_equal(lowpass_matrix(16, 4), B)\n", + "failure_message": "Check your implementation", + "hidden": false, + "locked": false, + "success_message": "Good, your implementation returns correct results" + }, + { + "code": ">>> with np.testing.assert_raises(ValueError):\n... lowpass_matrix(0, 0)\n>>> with np.testing.assert_raises(ValueError):\n... lowpass_matrix(16, -1)\n>>> with np.testing.assert_raises(ValueError):\n... lowpass_matrix(32, 17)\n", + "failure_message": "Did you forget to validate the input parameters before performing the computation ?", + "hidden": false, + "locked": false, + "success_message": "Good, you properly validated parameters before computing the result" + } + ], + "scored": true, + "setup": "", + "teardown": "", + "type": "doctest" + } + ] + }, + "q3": { + "name": "q3", + "points": null, + "suites": [ + { + "cases": [ + { + "code": ">>> assert w_c > w2 and w_c < w3\n", + "failure_message": "Check your value of w_c", + "hidden": false, + "locked": false, + "success_message": "Your value of w_c looks correct" + } + ], + "scored": true, + "setup": "", + "teardown": "", + "type": "doctest" + } + ] + }, + "q5": { + "name": "q5", + "points": null, + "suites": [ + { + "cases": [ + { + "code": ">>> B = np.eye(4)\n>>> B[1, 1] = 0\n>>> np.testing.assert_array_almost_equal(Bt_E(3, [1]), B)\n", + "failure_message": "Check your implementation", + "hidden": false, + "locked": false, + "success_message": "Good, your implementation returns correct results" + }, + { + "code": ">>> N = 5\n>>> E = [1, 3]\n>>> E2 = [1, 1, 3, 3, 3]\n>>> B = np.array([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n>>> np.testing.assert_array_almost_equal(Bt_E(N, E), B)\n>>> np.testing.assert_array_almost_equal(Bt_E(N, E2), B)\n", + "failure_message": "Check your implementation", + "hidden": false, + "locked": false, + "success_message": "Good, your implementation returns correct results" + }, + { + "code": ">>> with np.testing.assert_raises(ValueError):\n... Bt_E(10, [12, 5])\n>>> with np.testing.assert_raises(ValueError):\n... Bt_E(8, [2, -1])\n>>> with np.testing.assert_raises(ValueError):\n... Bt_E(5, [1, 2, 3, 4, 5])\n>>> with np.testing.assert_raises(ValueError):\n... Bt_E(0, [])\n", + "failure_message": "Did you forget to validate the input parameters before performing the computation ?", + "hidden": false, + "locked": false, + "success_message": "Good, you properly validated parameters before computing the result" + } + ], + "scored": true, + "setup": "", + "teardown": "", + "type": "doctest" + } + ] + }, + "q6": { + "name": "q6", + "points": null, + "suites": [ + { + "cases": [ + { + "code": ">>> N = 5\n>>> E = [1, 3]\n>>> E2 = [1, 1, 3, 3]\n>>> C = np.array([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n>>> np.testing.assert_array_almost_equal(C_E(N, E), C)\n>>> np.testing.assert_array_almost_equal(C_E(N, E2), C)\n", + "failure_message": "Check your implementation", + "hidden": false, + "locked": false, + "success_message": "Good, your implementation returns correct results" + }, + { + "code": ">>> with np.testing.assert_raises(ValueError):\n... C_E(10, [12, 5])\n>>> with np.testing.assert_raises(ValueError):\n... C_E(8, [2, -1])\n>>> with np.testing.assert_raises(ValueError):\n... C_E(5, [1, 2, 3, 4, 5])\n>>> with np.testing.assert_raises(ValueError):\n... C_E(0, [])\n", + "failure_message": "Did you forget to validate the input parameters before performing the computation ?", + "hidden": false, + "locked": false, + "success_message": "Good, you properly validated parameters before computing the result" + } + ], + "scored": true, + "setup": "", + "teardown": "", + "type": "doctest" + } + ] + } + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/solutions/week03/images/pocs.png b/solutions/week03/images/pocs.png new file mode 100644 index 0000000000000000000000000000000000000000..1802bed09435c3d7aea274cbe855941c3676c508 Binary files /dev/null and b/solutions/week03/images/pocs.png differ