{ "metadata": { "name": "", "signature": "sha256:2df71f183fc4894b48e69dfe04b31f3a3a64336f8f51cdf74438340a1a8c6642" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Deconvolution" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "A tutorial by Jan Willem de Gee (jwdegee@gmail.com)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Deconvolution is equivalent to selective averaging with correction for overlap between temporally adjacent responses (Dale, 1999), based on the assumption that hemodynamic / pupil responses superimpose linearly over time (Boynton et al., 1996). This analysis is implemented in for example Donner, Sagi, Bonneh & Heeger, JoN, 2008." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is Python, so let's start with importing some modules:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import os\n", "import numpy as np\n", "import scipy as sp\n", "import scipy.stats as stats\n", "import scipy.signal as signal\n", "import matplotlib.pyplot as plt\n", "from sympy import *\n", "import math" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 48 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's do inline plotting:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 49 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's first create and plot the true pupil response to a transient input. This is called an \"Inpulse Response Function\" (IRF)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# define an Impulse Response Function:\n", "def pupil_IRF(timepoints, s=1.0/(10**26), n=10.1, tmax=0.93):\n", " \n", " \"\"\" pupil_IRF defines the IRF (response to a transient input) of the pupil.\n", " \n", " Parameters\n", " ----------\n", " t: IRF is defined with respect to 't'\n", " s: scaling factor\n", " n: sets the width\n", " tmax: sets the time to peak \n", " IRF_len: function is evaluated for t = [0:IRF_len]\n", " \n", " Returns\n", " -------\n", " y: IRF evaluated for t = [0:IRF_len]\n", " yprime: IRF first derivative evaluated for t = [0:IRF_len]\n", " \n", " \"\"\"\n", " \n", " # in sympy:\n", " t = Symbol('t')\n", " y = ( (s) * (t**n) * (math.e**((-n*t)/tmax)) )\n", " yprime = y.diff(t)\n", " \n", " # lambdify:\n", " y = lambdify(t, y, \"numpy\")\n", " yprime = lambdify(t, yprime, \"numpy\")\n", " \n", " # evaluate:\n", " y = y(timepoints)\n", " yprime = yprime(timepoints)\n", " \n", " return (y, yprime)\n", "\n", "# create the IRF:\n", "sample_rate = 10\n", "IRF_len = 3.0 # in seconds\n", "timepoints = np.linspace(0,IRF_len,IRF_len*sample_rate)\n", "\n", "IRF, IRF_prime = pupil_IRF(timepoints=timepoints)\n", "IRF = IRF / IRF.std()\n", "IRF_prime = IRF_prime / IRF_prime.std()\n", "\n", "# plot the IRF:\n", "fig = plt.figure()\n", "plt.plot(timepoints, IRF, color='r')\n", "# plt.plot(timepoints, IRF_prime, color='g')\n", "plt.legend(['IRF'])\n", "plt.title('Impulse Response Function')\n", "plt.xlabel('time (s)')\n", "plt.ylabel('a.u.')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 50, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEZCAYAAACTsIJzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n6wAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 50 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's simulate convolved timeseries data based on this IRF." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# input:\n", "duration = 35 # in seconds\n", "times = np.array([1,6,11,11.5,16,16.5,21,22,26,27])\n", "input_signal = np.zeros(duration * sample_rate)\n", "for i in times:\n", " input_signal[i*sample_rate] = 1\n", "\n", "# convolve inputs with IRF: \n", "convolved_signal = (sp.convolve(input_signal, IRF, 'full'))[:-(IRF.shape[0]-1)]\n", "\n", "# let's add some noise:\n", "convolved_signal_noise = convolved_signal + np.random.normal(0,0.25,len(convolved_signal))\n", "\n", "timepoints = np.linspace(0,duration,duration*sample_rate)\n", "# plot simulated convolved signal with noise:\n", "fig = plt.figure()\n", "plt.plot(timepoints, convolved_signal_noise)\n", "for i in times:\n", " plt.axvline(i, color='r', alpha=0.5)\n", "plt.legend(['pupil time series'], loc=1)\n", "plt.title('simulated pupil time series, with measurement noise')\n", "plt.xlabel('time (s)')\n", "plt.ylabel('a.u.')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 53, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEZCAYAAACaWyIJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n", "text": [ "" ] } ], "prompt_number": 53 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's epoch the data and compute mean response." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# times for epoching:\n", "epoch_times = [0, 3] # in seconds\n", "\n", "# mean response:\n", "epochs = np.vstack([convolved_signal_noise[i+(epoch_times[0]*sample_rate):i+(epoch_times[1]*sample_rate)] for i in times*sample_rate])\n", "mean_response = np.mean(epochs, axis=0)\n", "\n", "# plot mean response versus IRF:\n", "timepoints = np.linspace(0,3,3*sample_rate)\n", "fig = plt.figure(figsize=(6,6))\n", "timepoints = np.linspace(epoch_times[0],epoch_times[1],(epoch_times[1]-epoch_times[0])*sample_rate)\n", "fig.add_subplot(211)\n", "for data in epochs:\n", " plt.plot(timepoints,data, color='b')\n", "plt.title('epoched responses')\n", "plt.xlabel('time from event (s)')\n", "plt.ylabel('a.u.')\n", "fig.add_subplot(212)\n", "plt.plot(timepoints, mean_response, color='b')\n", "plt.plot(timepoints, IRF, color='r')\n", "plt.legend(['mean epoched response', 'true response'])\n", "plt.title('mean response')\n", "plt.xlabel('time from event (s)')\n", "plt.ylabel('a.u.')\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAakAAAGrCAYAAAB65GhQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n", "text": [ "" ] } ], "prompt_number": 54 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is obviously not good... what we need to do is to is correct for for overlap between temporally adjacent responses...\n", "\n", "We'll have to try deconvolution.\n", "\n", "First make a design matrix:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# make design matrix:\n", "nr_samples = 3 * sample_rate # here we define the length of the deconvolution response we're interested in (30 samples = 3-s in our case).\n", "designMatrix = np.zeros((nr_samples, duration*sample_rate))\n", "for i in (times*sample_rate):\n", " for j in range(int(nr_samples)):\n", " designMatrix[j,i+j] = 1\n", "\n", "# plot design matrix:\n", "fig = plt.figure()\n", "plt.imshow(designMatrix.T, cmap='gray')\n", "plt.xticks([0,nr_samples])\n", "plt.title('design matrix')\n", "plt.xlabel('nr samples')\n", "plt.ylabel('length run')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 66, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAGYAAAEZCAYAAABl3FDCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUQRhGEUQhlEEYRjlfzBoI7SzY4MmAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 66 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's do deconvolution. \n", "\n", "For every regressor (in the above example, we have 30 regressors (the duration in samples of the response we are interested in) we want to find an associated scalar value (the \"beta\", $b$) that we can use to scale that particular regressor with, such that it best describes the measured data. In a deconvolution analysis, with a procedure called \"multiple regression\" we look for betas that minimimize the sum of squares of errors across all $k$ regressors in our design matrix at the same time.\n", "\n", "To do so, we set up the following equation (for a derivation, see all the way below):\n", "\n", "$b = (X'X)^{-1} X'y$\n", "\n", "In which,\n", "\n", "$b$ is a vector containing the betas (size: number of regressors; in the above example: 30). In the case of deconvolution, this vector is the actual deconvolved response to some input;\n", "\n", "$X$ is the design matrix (size: length measured time series x number of regressors);\n", "\n", "$y$ is the measured BOLD timeseries." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# deconvolution:\n", "designMatrix = np.mat(designMatrix).T\n", "deconvolved_response = ((designMatrix.T * designMatrix).I * designMatrix.T) * np.mat(convolved_signal_noise).T\n", "deconvolved_response = np.array(deconvolved_response)\n", "\n", "# plot deconvoled response versus true response:\n", "timepoints = np.linspace(0,3,3*sample_rate)\n", "fig = plt.figure(figsize=(6,6))\n", "fig.add_subplot(211)\n", "plt.plot(timepoints,deconvolved_response, color='b')\n", "plt.xlim(xmax=3)\n", "plt.ylim(ymin=-0.5, ymax=3.5)\n", "plt.legend(['deconvolved response'])\n", "plt.title('deconvolved response')\n", "plt.xlabel('time (s)')\n", "plt.ylabel('a.u.')\n", "fig.add_subplot(212)\n", "plt.plot(timepoints,IRF, color='r')\n", "plt.xlim(xmax=3)\n", "plt.ylim(ymin=-0.5, ymax=3.5)\n", "plt.legend(['true response'])\n", "plt.xlabel('time from event (s)')\n", "plt.ylabel('a.u.')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 67, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAGJCAYAAAB2Nm/HAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkR4AAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 67 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Derivation of the multiple regression equation:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In raw form the regression equation is:\n", "\n", "$y = a + b_1X_1 + b_2X_2 + ... + B_kX_k + e$\n", "\n", "This says that y, our dependent variable, is composed of a linear part and error. The linear part is composed of an intercept, a, and k independent variables, $X_1 ... X_k$ along with their associated regression weights $b_1 ... b_k$.\n", "\n", "In matrix terms, the same equation can be written:\n", "\n", "$y = X b + e$\n", "\n", "If we solve for the $b$ weights, we find that\n", "\n", "$b = (X'X)^{-1} X'y$\n", "\n", "To give you an idea why it looks like that, first remember the regression equation:\n", "\n", "$y = X b + e$\n", "\n", "Let's assume that error will equal zero on average. Now we can simply drop the error term, in order to sketch a proof:\n", "\n", "$y = Xb$\n", "\n", "Now we want to solve for $b$, so we need to get rid of $X$. First we will make $X$ into a square, symmetric matrix by premultiplying both sides of the equation by $X'$:\n", "\n", "$X'y = X'Xb$\n", "\n", "And now we have a square, symmetric matrix that with any luck has an inverse, which we will call $(X'X)^{-1}$. Multiply both sides by this inverse, and we have:\n", "\n", "$(X'X)^{-1} X'y = (X'X)^{-1} (X'X)b$\n", "\n", "It turns out that a matrix multiplied by its inverse is the identity matrix $(A^{-1}A=I)$:\n", "\n", "$(X'X)^{-1} X'y=Ib$\n", "\n", "and a matrix multiplied by the identity matrix is itself $(AI = IA = A)$:\n", "\n", "$(X'X)^{-1} X'y=b$\n", "\n", "which is the desired result." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }