{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# TP: Image Reconstruction in X-Ray Tomography " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# I Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "X-ray tomography reconstructs dense volumes of objects from a set of projections measured at different angles. The measurements\n", "$y\\in\\mathbb{R}^M$ and the sought absorption image $\\overline{x}\\in\\mathbb{R}^N$ obey the linear relation\n", "\\begin{equation}\n", "y = H \\overline{x} + w,\n", "\\label{eq:tomo_problem}\n", "\\end{equation}\n", "where $w \\in \\mathbb{R}^M$ is the measurement noise, that we assume i.i.d. Gaussian with variance $\\sigma^2$. The tomography matrix $H \\in \\mathbb{R}^{M \\times N}$ is sparse and encodes the geometry of the measurements. Here, we will focus on the case when $H$ models parallel projections of a 2-D\n", "object $\\overline{x}$. Tomography measures are acquired at fixed and regularly\n", "sampled rotational positions between the sample and the detector so that\n", "$H_{mn}$ models the intersection length between the $m$th light-ray and the\n", "$n$th pixel. If $N_\\theta$ is the number of different angular positions of the detector and $L$ the linear size of the detector, the number of measurements $M=L\\times\n", "N_\\theta$. In practice, the angular positions are regularly distributed on\n", "$[0,\\pi)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Traditional reconstruction methods such as the Filtered Back-Projection require the linear system\n", "to be sufficiently determined for good results, i.e., $N_\\theta \\sim L$. However, several applications could benefit from a smaller number of projections, either in order to reduce the total dose for medical applications, or to reduce the total acquisition time for in-situ experiments where the sample is evolving. Therefore, regularized reconstruction approaches must be developed in order to overcome the under-determinacy of the problem and to make it robust to the presence of noise in the measurements." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## I-1 Data generation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We do some imports and load the data:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import scipy\n", "from scipy.io import loadmat\n", "from scipy.sparse.linalg import LinearOperator, bicg\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import time\n", "from scipy.sparse import csr_matrix\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "H = loadmat(\"H.mat\")['H']\n", "x = loadmat(\"x.mat\")['x']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We simulate a sinogram y degraded by some noise. H is the projection matrix." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "z = H * x\n", "y = z + np.random.normal(scale=1.,size=z.shape)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "nx = 90;\n", "nt = 180;\n", "x_2D = x.reshape((nx,nx),order='F')\n", "y_2D = y.reshape((nx,nt),order='F')\n", "N = x.shape[0]" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.title(\"Sinogram\")\n", "plt.imshow(y_2D, cmap=\"gray\")\n", "\n", "plt.figure()\n", "plt.title(\"Original 2D object\")\n", "plt.imshow(x_2D, cmap=\"gray\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## I-2 Optimization Problem " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define the reconstructed image as the solution to the following optimization problem:\n", "\n", "$(\\forall x \\in \\mathbb{R}^N) \\quad f(x)=\\frac{1}{2}||Hx - y||^2 + \\lambda r(x)$\n", "\n", "where $r$ is a regularization function incorporating a priori assumptions to\n", "guarantee the robustness of the solution with respect to noise. In order to promote images formed by smooth regions separated by sharp edges, we set:\n", "\n", "$r(x) = \\sum^{2N}_{n=1} \\psi ([Gx]^{(n)})$ and $(\\forall u \\in \\mathbb{R}) \\quad \\psi(u) = \\sqrt{1 + u^2/\\delta^2}$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$G\\in \\mathbb{R}^{2N \\times N}$ is a sparse matrix computing discrete horizontal and vertical gradients of an image. \n", "$\\psi$ is a differentiable convex potential, applied elementwise, which can be viewed as a smoothed version of the absolute value." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "G = loadmat(\"G.mat\")['G']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Parameters $(\\lambda,\\delta)$ have been finetuned to ensure an optimal image quality (i.e., minimizing quadratic reconstruction error)." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "delta = 0.05\n", "lbd = 0.3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$f$ is differentiable on $\\mathbb{R}^N$. Its gradients reads:\n", "\n", "$\\nabla f(x) = H^THx - H^Ty + \\lambda G^T\\psi'(Gx)$\n", "with $\\forall u \\in \\mathbb{R} \\quad \\psi'(u) = \\frac{1}{\\delta^2}\\frac{u}{\\sqrt{1 + \\frac{u^2}{\\delta^2}}}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us define useful functions for function/gradient evaluation:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def psi(x, delta=delta): \n", " return np.sqrt(1 + np.square(x)/np.square(delta))\n", "\n", "def psi_prime(x, delta=delta):\n", " return x / (np.square(delta) * psi(x))\n", "\n", "def r(x):\n", " return psi(G.dot(x)).sum()\n", "\n", "def grad_r(x):\n", " return G.T.dot(psi_prime(G.dot(x)))\n", "\n", "def f(x):\n", " q = H.dot(x) - y\n", " return 0.5 * q.T.dot(q) + lbd * r(x)\n", "\n", "def grad_f(x):\n", " return H.T.dot(H.dot(x) - y) + lbd * grad_r(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$f$ is Lipschitz differentiable on $\\mathbb{R}^N$. The Lipschitz constant of $\\nabla f$ is\n", "\n", "$L = ||H||^2 + (\\lambda / \\delta^2)||G||^2$\n", "\n", "It can be computed as:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lipschitz constant = 16452.77\n" ] } ], "source": [ "# there is no norm 2 of matrix implemented with sparse matrix so we use a little trick to calculate it...\n", "lipschitz_cst = scipy.sparse.linalg.svds(H)[1].max()**2 + (lbd / delta**2) * scipy.sparse.linalg.svds(G)[1].max()**2\n", "print('Lipschitz constant = %.2f'%(lipschitz_cst))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# II Comparison of optimization algorithms" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Initialization of all algorithms:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "x_0 = np.zeros_like(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## II-1 Gradient Descent Algorithm " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us start with the gradient descent method. We will use a constant stepsize, defined as follows:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "nu = 1.999 / lipschitz_cst" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def gradient_descent(f, grad_f, x_0, nu):\n", " \n", " x_n = x_0\n", " grad_fx = grad_f(x_n)\n", " sqr_norm_grad = grad_fx.T.dot(grad_fx)\n", " it = 0\n", " \n", " history = []\n", " t_0 = time.time()\n", " history.append([time.time() - t_0, f(x_n)])\n", " \n", " # criterion\n", " while sqr_norm_grad > N * 1e-8:\n", " it += 1\n", " \n", " # iteration\n", " x_n = x_n - nu * grad_fx\n", " \n", " grad_fx = grad_f(x_n)\n", " sqr_norm_grad = grad_fx.T.dot(grad_fx)\n", " if it % 250 == 0:\n", " print(\"it \",it,\"sqr norm of grad:\", sqr_norm_grad[0,0])\n", " history.append([time.time() - t_0, f(x_n)])\n", " \n", " history.append([time.time() - t_0, f(x_n)])\n", " print(\"Converged in \", str(it), \" iterations\")\n", " \n", " return x_n, np.array(history)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "it 250 sqr norm of grad: 374.5081479969583\n", "it 500 sqr norm of grad: 9.034113593758054\n", "it 750 sqr norm of grad: 0.5326017231212149\n", "it 1000 sqr norm of grad: 0.050099691763915134\n", "it 1250 sqr norm of grad: 0.006185657434968036\n", "it 1500 sqr norm of grad: 0.0008848329799930624\n", "it 1750 sqr norm of grad: 0.00013676868143548245\n", "Converged in 1822 iterations\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\Emilie Chouzenoux\\Documents\\Anaconda\\lib\\site-packages\\ipykernel_launcher.py:28: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n" ] } ], "source": [ "x_rec, history_gradient_descent = gradient_descent(f, grad_f, x_0, nu)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.title(\"Reconstruction of x\")\n", "plt.imshow(x_rec.reshape(nx,nx,order='F'), cmap=\"gray\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## II-2 MM quadratic algorithm " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now implement an MM quadratic algorithm wich consists on minimizing, at each iteration, a quadratic majorant of $f$ at the current iterate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us construct a quadratic majorant of $f$:\n", "\n", "Using the properties of the course, we can deduce that, at $x' \\in \\mathbb{R}^N$, \n", "\n", "$f(x) \\leq q(x,x')$ with\n", "\n", "$q(x,x') = f(x') + <\\nabla f(x'),x-x'> + \\frac{1}{2}||x-x_0||_{A(x')}$\n", "\n", "The matrix $A(x')$ takes the form\n", "\n", "$A(x') = H^TH + \\lambda G^TD(G x') G$\n", "\n", "with\n", "\n", "$D(u) = \\mathrm{Diag}(\\frac{\\psi'(u_{i})}{u_{i}})$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define some functions that will be useful to evaluate the majorant function:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "# the diagonal matrix for the regularization function potential:\n", "def D(x):\n", " x = G.dot(x)\n", " d = 1. / (delta ** 2 * np.sqrt(1 + (x/delta)**2))\n", " return scipy.sparse.diags(d[:,0]).tocsc()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "# Returns a linear operator that does the computation of the curvature of the majorant matrix at some point\n", "def majorant_curve_operator(x_0):\n", " D_x_0 = D(x_0)\n", " def linear_operator(x):\n", " return H.T.dot(H.dot(x)) + lbd * G.T.dot(D_x_0.dot(G.dot(x)))\n", " return LinearOperator((N,N), matvec=linear_operator, rmatvec=linear_operator)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then implement the standard MM Quadratic Algorithm" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "# we use the constructed functions to implement the following algorithm:\n", "def mm_quadratic(f, grad_f, majorant_curve_operator, x_0, theta):\n", " x_n = x_0\n", " grad_fx = grad_f(x_n)\n", " sqr_norm_grad = grad_fx.T.dot(grad_fx)\n", " it = 0\n", " \n", " history = []\n", " t_0 = time.time()\n", " history.append([time.time() - t_0, f(x_n)])\n", " \n", " while sqr_norm_grad > N * 1e-8:\n", " it += 1\n", " \n", " # at each iteration solve the linear system instead of inverting the matrix:\n", " x_n = x_n - theta * bicg(majorant_curve_operator(x_n), grad_fx)[0].reshape(N,1)\n", " \n", " grad_fx = grad_f(x_n)\n", " sqr_norm_grad = grad_fx.T.dot(grad_fx)\n", " if it % 5 == 0:\n", " print(\"it \",it,\"sqr norm of grad:\", sqr_norm_grad[0,0])\n", " history.append([time.time() - t_0, f(x_n)])\n", " \n", " history.append([time.time() - t_0, f(x_n)])\n", " print(\"Converged in \", str(it), \" iterations\")\n", " \n", " return x_n, np.array(history)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "it 5 sqr norm of grad: 645.9171561642169\n", "it 10 sqr norm of grad: 13.566490281748383\n", "it 15 sqr norm of grad: 0.6741695900953164\n", "it 20 sqr norm of grad: 0.050832222214500136\n", "it 25 sqr norm of grad: 0.0049381029652942905\n", "it 30 sqr norm of grad: 0.0005694024766350623\n", "it 35 sqr norm of grad: 7.39652260088661e-05\n", "Converged in 35 iterations\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\Emilie Chouzenoux\\Documents\\Anaconda\\lib\\site-packages\\ipykernel_launcher.py:27: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n" ] } ], "source": [ "x_rec, history_mm_quadratic = mm_quadratic(f, grad_f, majorant_curve_operator, x_0, 1)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.title(\"Reconstruction of x\")\n", "plt.imshow(x_rec.reshape(nx,nx,order='F'), cmap=\"gray\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## II-3 3MG algorithm " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We rebuild similar functions and algorithm, adding the subspace limitation on the defined operators." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "def my_subspace_majorant_curv_matrix(x_0,dir_mat):\n", " D_x_0 = D(x_0)\n", " Gdir = G.dot(dir_mat)\n", " Hdir = H.dot(dir_mat)\n", " return Hdir.T.dot(Hdir) + lbd * Gdir.T.dot(D_x_0.dot(Gdir))" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "def three_mg_quadratic(f, grad_f, x_0):\n", " x_n = x_0\n", " x_n_minus_one = x_n\n", " grad_fx = grad_f(x_n)\n", " sqr_norm_grad = grad_fx.T.dot(grad_fx)\n", " it = 0\n", " \n", " history = []\n", " t_0 = time.time()\n", " history.append([time.time() - t_0, f(x_n)])\n", " \n", " while sqr_norm_grad > N * 1e-8:\n", " it += 1\n", " d1 = x_n - x_n_minus_one\n", " d2 = grad_fx\n", " dir_mat = np.concatenate((d1,d2),axis=1)\n", " x_n_minus_one = x_n\n", " \n", " # we solve the linear system on a limited subspace at each iteration:\n", " #x_n = x_n - dir_mat.dot(bicg(subspace_majorant_curve_operator(x_n, dir_mat), dir_mat.T.dot(grad_fx))[0].reshape(2,1))\n", " x_n = x_n - dir_mat.dot(scipy.linalg.pinv(my_subspace_majorant_curv_matrix(x_0,dir_mat))@dir_mat.T.dot(grad_fx))\n", " grad_fx = grad_f(x_n)\n", " sqr_norm_grad = grad_fx.T.dot(grad_fx)\n", " if it % 50 == 0:\n", " print(\"it \",it,\"sqr norm of grad:\", sqr_norm_grad[0,0])\n", " history.append([time.time() - t_0, f(x_n)])\n", " \n", " history.append([time.time() - t_0, f(x_n)])\n", " print(\"Converged in \", str(it), \" iterations\")\n", " \n", " return x_n, np.array(history)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "it 50 sqr norm of grad: 23.39751639767546\n", "it 100 sqr norm of grad: 0.022473989929391074\n", "it 150 sqr norm of grad: 0.00018532111044550486\n", "Converged in 159 iterations\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\Emilie Chouzenoux\\Documents\\Anaconda\\lib\\site-packages\\ipykernel_launcher.py:31: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n" ] } ], "source": [ "x_rec, history_three_mg_quadratic = three_mg_quadratic(f, grad_f, x_0)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.title(\"Reconstruction of x\")\n", "plt.imshow(x_rec.reshape(nx,nx,order='F'), cmap=\"gray\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## II-4 Parallel MM quadratic algorithm " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We finally implement a parallelizable version of the quadratic MM algorithm. One way to do this would be to find another majorant function, a \"diagonal\" majorant so that each term of the minimizer can be computed in parallel, independantly from the others, with no need of synchronization. Let us find $B$, such that $\\forall x \\in \\mathbb{R}^N \\quad A(x) \\preceq B(x)$, with $B(x)$ diagonal.\n", "\n", "Matrix $B(x)$ is constructed using Jensen's inequality.\n", "\n", "We have, \n", " \n", "$ H^TH \\preceq Diag(\\mathcal{h})$\n", "\n", "with $\\mathcal{h}_i = \\sum_{m=1}^M |H_{mi}| \\sum_{p=1}^N |H_{mp}|$\n", "\n", "Similarly, for every $x' \\in \\mathbb{R}^N$,\n", "\n", "$G^{T} D(G x')G \\preceq Diag(\\mathcal{g}(x'))$ \n", "\n", "with $\\mathcal{g}_i(x') = \\sum_{n=1}^{2N} \\frac{\\psi'(Gx')_{n}}{(Gx')_{n}} |G_{ni}| \\sum_{p=1}^{n} |G_{np}|$\n", "\n", "We finally obtain:\n", "\n", "$\n", "A(x') \\preceq Diag(\\mathcal{h}) + \\lambda Diag(\\mathcal{g}(x'))\n", "$" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "H_diag = H.multiply(H.dot(np.ones((N,1)))).T.dot(np.ones((H.shape[0],1)))" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "G_diag = G.multiply(G.dot(np.ones((N,1))))" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "def b_diag_inverse(x):\n", " return scipy.sparse.diags(1./(H_diag + lbd * G_diag.T.dot(D(x).diagonal()))[0]).tocsc()" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "def mm_quadratic_parallel(f, grad_f, b_diag_inverse, x_0, theta):\n", " x_n = x_0\n", " grad_fx = grad_f(x_n)\n", " sqr_norm_grad = grad_fx.T.dot(grad_fx)\n", " it = 0\n", " \n", " history = []\n", " t_0 = time.time()\n", " history.append([time.time() - t_0, f(x_n)])\n", " \n", " while sqr_norm_grad > N * 1e-8:\n", " it += 1\n", " x_n = x_n - theta * b_diag_inverse(x_n).dot(grad_fx) \n", " grad_fx = grad_f(x_n)\n", " sqr_norm_grad = grad_fx.T.dot(grad_fx)\n", " if it % 200 == 0:\n", " print(\"it \",it,\"sqr norm of grad:\", sqr_norm_grad[0,0])\n", " history.append([(time.time() - t_0)/32., f(x_n)])\n", " \n", " history.append([(time.time() - t_0)/32., f(x_n)])\n", " print(\"Converged in \", str(it), \" iterations\")\n", " \n", " return x_n, np.array(history)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that, in order to have an idea of the potential performance of the parallel algorithm, we consider that the computation is distributed on 32 workers and we neglect the overhead, so we will have a rough idea of the computational performance on a multicore architecture." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "it 200 sqr norm of grad: 1600.1544924034229\n", "it 400 sqr norm of grad: 64.0093506661173\n", "it 600 sqr norm of grad: 5.790370534866147\n", "it 800 sqr norm of grad: 0.7697509678692972\n", "it 1000 sqr norm of grad: 0.13187364538618282\n", "it 1200 sqr norm of grad: 0.02691076491041504\n", "it 1400 sqr norm of grad: 0.0061659528212988195\n", "it 1600 sqr norm of grad: 0.0015211504982393308\n", "it 1800 sqr norm of grad: 0.00039317665740917166\n", "it 2000 sqr norm of grad: 0.00010468707332300359\n", "Converged in 2040 iterations\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\Emilie Chouzenoux\\Documents\\Anaconda\\lib\\site-packages\\ipykernel_launcher.py:23: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n" ] } ], "source": [ "x_rec, history_mm_quadratic_parallel = mm_quadratic_parallel(f, grad_f, b_diag_inverse, x_0, 0.99)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# III Comparison of the methods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We plot the evolution of the $f - f_{min}$ in function of time for the differents algorithms." ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "14683.215886288155\n" ] } ], "source": [ "min_objective = np.min(history_three_mg_quadratic[:,1])\n", "print(min_objective.item())" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.semilogy(history_three_mg_quadratic[:,0],history_three_mg_quadratic[:,1]-min_objective.item(), label = \"3MG quadratic\")\n", "plt.semilogy(history_gradient_descent[:,0], history_gradient_descent[:,1]-min_objective.item(), label = \"gradient descent\")\n", "plt.semilogy(history_mm_quadratic[:,0],history_mm_quadratic[:,1]-min_objective.item(), label = \"MM quadratic\")\n", "plt.semilogy(history_mm_quadratic_parallel[:,0],history_mm_quadratic_parallel[:,1]-min_objective.item(), label = \"Parallel (32 workers)\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see how much time it took to converge for the different algorithms." ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "With the given criteria, algorithms took the following time to converge:\n", "Gradient descent: 26 s\n", "MM quadratic: 37 s\n", "3MG quadratic: 5 s\n", "Parallel (32 workers): 17 s\n" ] } ], "source": [ "print(\"With the given criteria, algorithms took the following time to converge:\")\n", "print(\"Gradient descent: {} s\".format(int(history_gradient_descent[-1,0])))\n", "print(\"MM quadratic: {} s\".format(int(history_mm_quadratic[-1,0])))\n", "print(\"3MG quadratic: {} s\".format(int(history_three_mg_quadratic[-1,0])))\n", "print(\"Parallel (32 workers): {} s\".format(int(history_mm_quadratic_parallel[-1,0])))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bibliography\n", "\n", "* A. Kak and M. Slaney, Principles of computerized tomographic imaging, Classics in Applied Mathematics. SIAM, Philadelphia, 1988.\n", "\n", "* A. H. Delaney and Y. Bresler, “Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography,” IEEE Transactions on Image Processing, vol. 7, no. 2, pp. 204 –221, Feb. 1998.\n", "\n", "* E. Chouzenoux, F. Zolyniak, E. Gouillart and H. Talbot. A Majorize-Minimize Memory Gradient Algorithm Applied to X-Ray Tomography. In Proceedings of the 20th IEEE International Conference on Image Processing (ICIP 2013), pp. 1011-1015, Melbourne, Australia, 15-18 sep. 2013" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 2 }