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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Populating the interactive namespace from numpy and matplotlib\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%pylab inline\n", | |
| "from scipy import signal" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQYAAAD8CAYAAACVSwr3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAADIJJREFUeJzt3F+MnXWdx/H3Z2mpWcRAxW1qaRY03Yt6YW0mhURi2JAV6E3xhsCFNIZkvCiJJu5F1Qu5dDerJiS7JDUSy8aFJSqhF+wqNCZkL0AGUksLIiOW0G5p18UgWZPa4ncv5ike+5thpnPOM+fM7vuVnJzn/M5z5nz7pHnn/E9VIUmD/mzcA0iaPIZBUsMwSGoYBkkNwyCpYRgkNXoLQ5JbkrycZDbJ3r7uR9LopY/PMSS5BPgF8DfAceBZ4M6qenHkdyZp5Pp6xLADmK2qV6vq98DDwK6e7kvSiK3p6e9uAl4fuHwcuG6hnS/Nunofl/U0iiSAt/nNr6vqQ0vZt68wLCrJNDAN8D7+nOty07hGkf5feLK+/9pS9+3rqcQJYPPA5au7tXdV1b6qmqqqqbWs62kMScvRVxieBbYkuTbJpcAdwIGe7kvSiPXyVKKqziW5B/gRcAnwQFUd7eO+JI1eb68xVNXjwON9/X1J/fGTj5IahkFSwzBIahgGSQ3DIKlhGCQ1DIOkhmGQ1DAMkhqGQVLDMEhqGAZJDcMgqWEYJDUMg6SGYZDUMAySGoZBUsMwSGoYBkkNwyCpYRgkNQyDpIZhkNQwDJIahkFSwzBIahgGSQ3DIKlhGCQ1DIOkhmGQ1DAMkhqGQVJjzTA3TnIMeBt4BzhXVVNJ1gP/ClwDHANur6rfDDempJU0ikcMf11V26pqqru8FzhYVVuAg91lSatIH08ldgH7u+39wG093IekHg0bhgJ+nOS5JNPd2oaqOtltvwFsmO+GSaaTzCSZOcuZIceQNEpDvcYA3FBVJ5L8BfBEkp8PXllVlaTmu2FV7QP2AXwg6+fdR9J4DPWIoapOdOengUeBHcCpJBsBuvPTww4paWUtOwxJLkty+flt4NPAEeAAsLvbbTfw2LBDSlpZwzyV2AA8muT83/mXqvr3JM8CjyS5G3gNuH34MSWtpGWHoapeBT4+z/p/AzcNM5Sk8fKTj5IahkFSwzBIahgGSQ3DIKlhGCQ1DIOkhmGQ1DAMkhqGQVLDMEhqGAZJDcMgqWEYJDUMg6SGYZDUMAySGoZBUsMwSGoYBkkNwyCpYRgkNQyDpIZhkNQwDJIahkFSwzBIahgGSQ3DIKlhGCQ1DIOkhmGQ1DAMkhqLhiHJA0lOJzkysLY+yRNJXunOr+zWk+S+JLNJDifZ3ufwkvqxlEcM3wVuuWBtL3CwqrYAB7vLALcCW7rTNHD/aMaUtJIWDUNVPQW8ecHyLmB/t70fuG1g/cGa8zRwRZKNoxpW0spY7msMG6rqZLf9BrCh294EvD6w3/FuTdIqMvSLj1VVQF3s7ZJMJ5lJMnOWM8OOIWmElhuGU+efInTnp7v1E8Dmgf2u7tYaVbWvqqaqamot65Y5hqQ+LDcMB4Dd3fZu4LGB9bu6dyeuB94aeMohaZVYs9gOSR4CbgSuSnIc+BrwdeCRJHcDrwG3d7s/DuwEZoHfAZ/rYWZJPVs0DFV15wJX3TTPvgXsGXYoSePlJx8lNQyDpIZhkNQwDJIahkFSwzBIahgGSQ3DIKlhGCQ1DIOkhmGQ1DAM6tWP/vPQuEfQMhgG9ermD28b9whaBsMgqWEYJDUMg6SGYZDUMAySGoZBUsMwSGoYBkkNwyCpYRgkNQyDpIZhkNQwDJIahkFSwzBIahgGSQ3DIKlhGCQ1DIOkhmGQ1DAMkhqLhiHJA0lOJzkysHZvkhNJDnWnnQPXfTnJbJKXk9zc1+CS+rOURwzfBW6ZZ/1bVbWtOz0OkGQrcAfwse42/5TkklENK2llLBqGqnoKeHOJf28X8HBVnamqXwGzwI4h5pM0BsO8xnBPksPdU40ru7VNwOsD+xzv1hpJppPMJJk5y5khxpA0assNw/3AR4FtwEngGxf7B6pqX1VNVdXUWtYtcwxJfVhWGKrqVFW9U1V/AL7NH58unAA2D+x6dbcmaRVZVhiSbBy4+Bng/DsWB4A7kqxLci2wBfjpcCNKWmlrFtshyUPAjcBVSY4DXwNuTLINKOAY8HmAqjqa5BHgReAcsKeq3ulndEl9SVWNewY+kPV1XW4a9xjS/2lP1vefq6qppezrJx8lNQyDpIZhkNQwDJIahkFSwzBIahgGSQ3DIKlhGCQ1DIOkhmGQ1DAMkhqGQVLDMEhqGAZJDcMgqWEYJDUMg6SGYZDUMAySGoZBUsMwSGoYBkkNwyCpYRgkNQyDpIZhkNQwDJIahkFSwzBIahgGSQ3DIKlhGCQ1Fg1Dks1JfpLkxSRHk3yhW1+f5Ikkr3TnV3brSXJfktkkh5Ns7/sfIWm0lvKI4RzwparaClwP7EmyFdgLHKyqLcDB7jLArcCW7jQN3D/yqSX1atEwVNXJqnq+234beAnYBOwC9ne77Qdu67Z3AQ/WnKeBK5JsHPnkknpzUa8xJLkG+ATwDLChqk52V70BbOi2NwGvD9zseLcmaZVYchiSvB/4AfDFqvrt4HVVVUBdzB0nmU4yk2TmLGcu5qaSerakMCRZy1wUvldVP+yWT51/itCdn+7WTwCbB25+dbf2J6pqX1VNVdXUWtYtd35JPVjKuxIBvgO8VFXfHLjqALC7294NPDawflf37sT1wFsDTzkkrQJrlrDPJ4HPAi8kOdStfQX4OvBIkruB14Dbu+seB3YCs8DvgM+NdGJJvVs0DFX1H0AWuPqmefYvYM+Qc0kaIz/5KKlhGCQ1DIOkhmGQ1DAMkhqGQVLDMEhqGAZJDcMgqWEYJDUMg6SGYZDUMAySGoZBUsMwSGoYBkkNwyCpYRgkNQyDpIZhkNQwDJIahkFSwzBIahgGSQ3DIKlhGCQ1DIOkhmGQ1DAMkhqGQVLDMEhqGAZJDcMgqWEYJDUWDUOSzUl+kuTFJEeTfKFbvzfJiSSHutPOgdt8OclskpeT3NznP0DS6K1Zwj7ngC9V1fNJLgeeS/JEd923quofBndOshW4A/gY8GHgySR/VVXvjHJwSf1Z9BFDVZ2sque77beBl4BN73GTXcDDVXWmqn4FzAI7RjGspJVxUa8xJLkG+ATwTLd0T5LDSR5IcmW3tgl4feBmx5knJEmmk8wkmTnLmYseXFJ/lhyGJO8HfgB8sap+C9wPfBTYBpwEvnExd1xV+6pqqqqm1rLuYm4qqWdLCkOStcxF4XtV9UOAqjpVVe9U1R+Ab/PHpwsngM0DN7+6W5O0SizlXYkA3wFeqqpvDqxvHNjtM8CRbvsAcEeSdUmuBbYAPx3dyJL6tpR3JT4JfBZ4Icmhbu0rwJ1JtgEFHAM+D1BVR5M8ArzI3Dsae3xHQlpdUlXjnoEk/wX8D/Drcc+yBFexOuaE1TOrc47efLP+ZVV9aCk3nogwACSZqaqpcc+xmNUyJ6yeWZ1z9Iad1Y9ES2oYBkmNSQrDvnEPsESrZU5YPbM65+gNNevEvMYgaXJM0iMGSRNi7GFIckv39ezZJHvHPc+FkhxL8kL31fKZbm19kieSvNKdX7nY3+lhrgeSnE5yZGBt3rky577uGB9Osn0CZp24r+2/x08MTNRxXZGfQqiqsZ2AS4BfAh8BLgV+Bmwd50zzzHgMuOqCtb8H9nbbe4G/G8NcnwK2A0cWmwvYCfwbEOB64JkJmPVe4G/n2Xdr9/9gHXBt9//jkhWacyOwvdu+HPhFN89EHdf3mHNkx3Tcjxh2ALNV9WpV/R54mLmvbU+6XcD+bns/cNtKD1BVTwFvXrC80Fy7gAdrztPAFRd8pL1XC8y6kLF9bb8W/omBiTqu7zHnQi76mI47DEv6ivaYFfDjJM8lme7WNlTVyW77DWDDeEZrLDTXpB7nZX9tv28X/MTAxB7XUf4UwqBxh2E1uKGqtgO3AnuSfGrwypp7rDZxb+1M6lwDhvrafp/m+YmBd03ScR31TyEMGncYJv4r2lV1ojs/DTzK3EOwU+cfMnbnp8c34Z9YaK6JO841oV/bn+8nBpjA49r3TyGMOwzPAluSXJvkUuZ+K/LAmGd6V5LLut+5JMllwKeZ+3r5AWB3t9tu4LHxTNhYaK4DwF3dq+jXA28NPDQei0n82v5CPzHAhB3XheYc6TFdiVdRF3mFdSdzr6r+EvjquOe5YLaPMPdq7s+Ao+fnAz4IHAReAZ4E1o9htoeYe7h4lrnnjHcvNBdzr5r/Y3eMXwCmJmDWf+5mOdz9x904sP9Xu1lfBm5dwTlvYO5pwmHgUHfaOWnH9T3mHNkx9ZOPkhrjfiohaQIZBkkNwyCpYRgkNQyDpIZhkNQwDJIahkFS438BkVhp+jb+Ds8AAAAASUVORK5CYII=\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "image = np.zeros((256, 256))\n", | |
| "image[30,50] = 1\n", | |
| "image[120,140] = 1\n", | |
| "imshow(image)\n", | |
| "show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "(256, 256)\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "k = signal.windows.gaussian(image.shape[0], std=5)\n", | |
| "k2 = np.outer(k,k)\n", | |
| "x = signal.convolve2d(image, k2, mode='same')\n", | |
| "imshow(x)\n", | |
| "print(x.shape)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def fftdeconvolve(in1, in2, mode=\"full\"):\n", | |
| " \"\"\"Deconvolve two N-dimensional arrays using FFT. See convolve.\n", | |
| "\n", | |
| " \"\"\"\n", | |
| "\n", | |
| " IN1 = np.fft.fftn(in1) / np.fft.fftn(in2)\n", | |
| "\n", | |
| " ret = np.fft.ifftn(IN1).copy()\n", | |
| "\n", | |
| " return np.nan_to_num(ret.real)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in true_divide\n", | |
| " \n", | |
| "/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: invalid value encountered in true_divide\n", | |
| " \n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "0.0" | |
| ] | |
| }, | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": "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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "a = fftdeconvolve(x, k2)\n", | |
| "imshow(a)\n", | |
| "a.max()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "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": "3.7.2" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Populating the interactive namespace from numpy and matplotlib\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%pylab inline\n", | |
| "from scipy import signal" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": "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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "image = np.zeros((256, 256))\n", | |
| "image[30,50] = 1\n", | |
| "image[120,140] = 1\n", | |
| "imshow(image)\n", | |
| "show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "(256, 256)\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "k = signal.windows.gaussian(image.shape[0], std=5)\n", | |
| "k2 = np.outer(k,k)\n", | |
| "x = signal.convolve2d(image, k2, mode='same')\n", | |
| "imshow(x)\n", | |
| "print(x.shape)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def fftdeconvolve(in1, in2, mode=\"full\"):\n", | |
| " \"\"\"Deconvolve two N-dimensional arrays using FFT. See convolve.\n", | |
| "\n", | |
| " \"\"\"\n", | |
| "\n", | |
| " IN1 = np.fft.fftn(in1) / np.fft.fftn(in2)\n", | |
| "\n", | |
| " ret = np.fft.ifftn(IN1).copy()\n", | |
| "\n", | |
| " return np.nan_to_num(ret.real)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in true_divide\n", | |
| " \n", | |
| "/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: invalid value encountered in true_divide\n", | |
| " \n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "0.0" | |
| ] | |
| }, | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": "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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "a = fftdeconvolve(x, k2)\n", | |
| "imshow(a)\n", | |
| "a.max()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "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": "3.7.2" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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