{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# 2-D Daubechies Wavelets" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This numerical tour explores 2-D multiresolution analysis \n", "with Daubchies wavelet transform.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) for details about how to install the toolboxes." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/gpeyre/anaconda/envs/p34/lib/python3.4/site-packages/IPython/core/magics/pylab.py:161: UserWarning: pylab import has clobbered these variables: ['pylab']\n", "%matplotlib prevents importing * from pylab and numpy\n", " \"\\n%matplotlib prevents importing * from pylab and numpy\"\n" ] } ], "source": [ "from __future__ import division\n", "from nt_toolbox.general import *\n", "from nt_toolbox.signal import *\n", "%pylab inline\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Wavelets Filters" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The 2-D wavelet transform of a continuous image $f(x)$ computes the set\n", "of inner products \n", "$$d_j^k[n] = \\dotp{f}{\\psi_{j,n}^k}$$ \n", "for scales $j \\in \\ZZ$, position $n \\in \\ZZ^2$ and orientation $k \\in \\{H,V,D\\}$.\n", "\n", "\n", "The wavelet atoms are defined by scaling and translating three mother\n", "atoms $\\{\\psi^H,\\psi^V,\\psi^D\\}$:\n", "$$\\psi_{j,n}^k(x) = \\frac{1}{2^j}\\psi^k \\left( \\frac{x-2^j n}{2^j} \\right)$$\n", "These oriented wavelets are defined by a tensor product of a 1-D wavelet\n", "function $\\psi(t)$ and a 1-D scaling function $\\phi(t)$\n", "$$\\psi^H(x)=\\phi(x_1)\\psi(x_2), \\quad \\psi^V(x)=\\psi(x_1)\\phi(x_2)\n", "\\qandq \\psi^D(x)=\\psi(x_1)\\psi(x_2).$$\n", "\n", "\n", "The fast wavelet transform algorithm does not make use of the wavelet and scaling functions,\n", "but of the filters $h$ and $g$ that caracterize their interaction:\n", "$$g[n] = \\frac{1}{\\sqrt{2}}\\dotp{\\psi(t/2)}{\\phi(t-n)} \n", "\\qandq h[n] = \\frac{1}{\\sqrt{2}}\\dotp{\\phi(t/2)}{\\phi(t-n)}.$$\n", "\n", "\n", "The simplest filters are the Haar filters\n", "$$h = [1, 1]/\\sqrt{2} \\qandq g = [-1, 1]/\\sqrt{2}.$$\n", "\n", "\n", "Daubechies wavelets extends the haar wavelets by using longer\n", "filters, that produce smoother scaling functions and wavelets.\n", "Furthermore, the larger the size $p=2k$ of the filter, the higher is the number\n", "$k$ of vanishing moment. \n", "\n", "A high number of vanishing moments allows to better compress regular\n", "parts of the signal. However, increasing the number of vanishing moments\n", "also inceases the size of the support of the wavelets, wich can be\n", "problematic in part where the signal is singular (for instance\n", "discontinuous).\n", "\n", "Choosing the _best_ wavelet, and thus choosing $k$, that is adapted to a\n", "given class of signals, thus corresponds to \n", "a tradeoff between efficiency in regular and singular parts.\n", "\n", "- The filter with $k=1$ vanishing moments corresponds to the Haar filter.\n", "- The filter with $k=2$ vanishing moments corresponds to the famous |D4| wavelet, which compresses perfectly linear signals.\n", "- The filter with $k=3$ vanishing moments compresses perfectly quadratic signals." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Select the low pass filter. We start with the Daubechies 4 filter. Note that the filter should have odd \n", "length, so we zero-padd it." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "h = [0, .482962913145, .836516303738, .224143868042, -.129409522551] \n", "h = h/norm(h)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Note that the high pass filter $g$ is computed directly from the low pass filter as:\n", "$$g[n] = (-1)^{1-n}h[1-n].$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "u = power(-ones(len(h)-1),range(1,len(h))) # alternate +1/-1\n", "g = concatenate(([0], h[-1:0:-1] * u))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 0.48296291 0.8365163 0.22414387 -0.12940952]\n", "[ 0. 0.12940952 0.22414387 -0.8365163 0.48296291]\n" ] } ], "source": [ "print(h)\n", "print(g)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Up and Down Filtering" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The basic wavelet operation is low/high filtering, followed by down sampling. \n", "\n", "Starting from some 1-D signal $f \\in \\RR^N$, one thus compute the\n", "low pass signal $a \\in \\RR^{N/2}$ and the high pass \n", "signal $d \\in \\RR^{N/2}$ as\n", "$$a = (f \\star h) \\downarrow 2 \\qandq \n", "d = (f \\star g) \\downarrow 2$$\n", "where the sub-sampling is defined as \n", "$$(u \\downarrow 2)[k] = u[2k].$$\n", "\n", "Create a random signal $f \\in \\RR^N$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "N = 256\n", "f = rand(N,1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Low/High pass filtering followed by sub-sampling." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "a = subsampling( cconv(f,h,1),1 )\n", "d = subsampling( cconv(f,g,1),1 )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "For orthogonal filters, the reverse of this process is its dual\n", "(aka its transpose), which is upsampling followed by low/high pass\n", "filtering with the reversed filters and summing:\n", "$$(a \\uparrow h) \\star \\tilde h + (d \\uparrow g) \\star \\tilde g = f$$\n", "where $\\tilde h[n]=h[-n]$ (computed modulo $N$) and \n", "$(u \\uparrow 2)[2n]=u[n]$ and $(u \\uparrow 2)[2n+1]=0$.\n", "\n", "Perform the up-sampling followed by filtering." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "f1 = cconv(upsampling(a,1),reverse(h),1) + cconv(upsampling(d,1),reverse(g),1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Check that we really recover the same signal." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.469343188183937e-13\n" ] } ], "source": [ "print( norm(f-f1)/norm(f) )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Forward 2-D Wavelet transform" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The set of wavelet coefficients are computed with a fast algorithm that\n", "exploits the embedding of the approximation spaces $V_j$ spanned by the \n", "scaling function $\\{ \\phi_{j,n} \\}_n$ defined as\n", "$$\\phi_{j,n}(x) = \\frac{1}{2^j}\\phi^0\\pa{\\frac{x-2^j n}{2^j}} \n", "\\qwhereq \\phi^0(x)=\\phi(x_1)\\phi(x_2).$$\n", "\n", "The wavelet transform of $f$ is computed by using intermediate discretized low\n", "resolution images obtained by projection on the spaces $V_j$:\n", "$$a_j[n] = \\dotp{f}{\\phi_{j,n}}.$$" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Load a gray-scale image $f$ of $n \\times n$ pixels. " ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/gpeyre/anaconda/envs/p34/lib/python3.4/site-packages/skimage/transform/_warps.py:84: UserWarning: The default mode, 'constant', will be changed to 'reflect' in skimage 0.15.\n", " warn(\"The default mode, 'constant', will be changed to 'reflect' in \"\n" ] } ], "source": [ "n = 256\n", "name = 'nt_toolbox/data/flowers.png'\n", "f = load_image(name, n)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the image $f$." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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WC5VKRWpueO0kUEl+qlmOXC4ntRokhguFAsrlsoSirKJVSWF1qOiTAjfOF0Mk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\nwWDQvMxGo2GdzfHaGJ7T6XQUjUb17LPP6ktf+pKNW3jcdSEUAxyDTqdjV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imageplot(f, 'Original image')" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f0 = f\n", "f1 = f.flatten()\n", "f1[ argsort(f0.flatten()) ] = np.linspace(0,1,n*n)\n", "hist(f1.flatten())\n", "I = argsort(f0.flatten())" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The algorithm starts at the coarsest scale $j=\\log_2(n)-1$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "j = int(log2(n)-1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The first step of the algorithm perform filtering/downsampling in the\n", "horizontal direction.\n", "\n", "$$\\tilde a_{j-1} = (a_j \\star^H h) \\downarrow^{2,H} \\qandq \n", " \\tilde d_{j-1} = (a_j \\star^H g) \\downarrow^{2,H}$$\n", "\n", "Here, the operator $\\star^H$ and $\\downarrow^{2,H}$\n", "are defined by applying $\\star$ and $\\downarrow^2$\n", "to each column of the matrix.\n", "\n", "The second step computes the filtering/downsampling in the vertical\n", "direction.\n", "\n", "$$a_{j-1} = (\\tilde a_j \\star^V h) \\downarrow^{2,V} \\qandq \n", " d_{j-1}^V = (\\tilde a_j \\star^V g) \\downarrow^{2,V},$$\n", "$$d_{j-1}^H = (\\tilde d_j \\star^V h) \\downarrow^{2,V} \\qandq \n", " d_{j-1}^D = (\\tilde d_j \\star^V g) \\downarrow^{2,V}.$$\n", " \n", "A wavelet transform is\n", "computed by iterating high pass and loss pass filterings with |h| and |g|, followed by sub-samplings.\n", "Since we are in 2-D, we need to compute these filterings+subsamplings\n", "in the horizontal and then in the vertical direction (or\n", "in the reverse order, it does not mind).\n", "\n", "Initialize the transformed coefficients as the image itself and set the\n", "initial scale as the maximum one.\n", "fW will be iteratively transformated and will contains the\n", "coefficients." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "fW = f.copy()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Select the sub-part of the image to transform." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "A = fW[:2**(j+1):,:2**(j+1):]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Apply high and low filtering+subsampling in the vertical direction (1st ooordinate),\n", "to get coarse and details." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Coarse = subsampling(cconv(A,h,1),1)\n", "Detail = subsampling(cconv(A,g,1),1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Concatenate them in the vertical direction to get the result." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "A = concatenate( (Coarse, Detail), axis=0 )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the result of the vertical transform." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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Q6/XweDw/Aqe+2bgnEM2BAwcmd+/ejdnZWTgcDjgcDqRSKfHa8vk8YrEYhoaG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Sw1qQzRoMAxWFw3r/etCyKRiDljOD+ePebbMSeTSbW2ttprgEJwgoBHaKFNdMB3IdMeosxkMibj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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imageplot(f, 'Original image', [1,2,1])\n", "imageplot(A, 'First step', [1,2,2])" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Apply high and low filtering+subsampling in the horizontal direction (2nd ooordinate),\n", "to get coarse and details." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Coarse = subsampling(cconv(A,h,2),2)\n", "Detail = subsampling(cconv(A,g,2),2)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Concatenate them in the horizontal direction to get the result." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "A = concatenate( (Coarse, Detail), axis=1 )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Assign the transformed data." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "fW[:2**(j+1):,:2**(j+1):] = A" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the result of the horizontal transform." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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FzMzMSNOdRCIhVabEIRgKsl3g2bNn0Ww2pQEP+SoMH86cOYPvfOc7GBoakmvk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\nu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_wavelet(fW,j);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Implement a full wavelet transform that extract iteratively wavelet\n", "coefficients, by repeating these steps. Take care of choosing the\n", "correct number of steps." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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9YtdpELHAtNlsWuYtJkder5dqtUpHRwfLy8tkMhlVKsjkuLGxgcViYWJigmKx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\n1uJSiFWvrDOZDFdccQU9PT3KoBB80263873vfY/PfvazakYQD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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Jmin = 0\n", "Jmax = log2(n)-1\n", "fW = f.copy()\n", "for j in arange(Jmax,Jmin-1,-1):\n", " A = fW[:2**(j+1):,:2**(j+1):]\n", " for d in arange(1,3):\n", " Coarse = subsampling(cconv(A,h,d),d)\n", " Detail = subsampling(cconv(A,g,d),d)\n", " A = concatenate( (Coarse, Detail), axis=d-1 )\n", " fW[:2**(j+1):,:2**(j+1):] = A\n", " j1 = Jmax-j\n", " if j1<4:\n", " subplot(3,4, j1 + 1)\n", " imageplot(A[:2**j:,2**j:2**(j+1):], 'H,j=' + str(int(j)) )\n", " subplot(3,4, j1 + 5)\n", " imageplot(A[2**j:2**(j+1):,:2**j:], 'V,j=' + str(int(j)) )\n", " subplot(3,4, j1 + 9)\n", " imageplot(A[2**j:2**(j+1):,2**j:2**(j+1):], 'D,j=' + str(int(j)))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Check for orthogonality of the transform (conservation of energy)." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Energy of the signal/coefficients = 0.999999999996\n" ] } ], "source": [ "print( 'Energy of the signal/coefficients = ' + str(norm(f)/norm(fW)) )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the wavelet coefficients." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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fLvL+/n58Ph+Tk5MsLCzooj116hTT09MsLCywtLTE/Pw8b33rWzl+/DixWIw3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36/H9VqVepWNMgKGLEOfgYNYbfbRSwWg8vlgt1ux+TkJLrdLpaXl5HJZCS84uYevhYNAYFV4j36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\nSH5GfOB6nYVn/O0JL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_wavelet(fW,Jmin);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Inverse 2-D Wavelet transform" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Inversing the wavelet transform means retrieving a signal f1 from the\n", "coefficients fW. If fW are exactely the coefficients of f, then\n", "f=f1 up to machine precision. \n", "\n", "Initialize the image to recover f1 as the transformed coefficient, and\n", "select the smallest possible scale." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "f1 = fW.copy()\n", "j = 0" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Select the sub-coefficient to transform." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "A = f1[:2**(j+1):,:2**(j+1):]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Retrieve coarse and detail coefficients in the vertical direction (you\n", "can begin by the other direction, this has no importance)." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Coarse = A[:2**j:,:]\n", "Detail = A[2**j:2**(j+1):,:]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Undo the transform by up-sampling and then dual filtering." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Coarse = cconv(upsampling(Coarse,1),reverse(h),1)\n", "Detail = cconv(upsampling(Detail,1),reverse(g),1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Recover the coefficient by summing." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "A = Coarse + Detail" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Retrieve coarse and detail coefficients in the vertical direction (you\n", "can begin by the other direction, this has no importance)." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Coarse = A[:,:2**j:]\n", "Detail = A[:,2**j:2**(j+1):]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Undo the transform by up-sampling and then dual filtering." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Coarse = cconv(upsampling(Coarse,2),reverse(h),2)\n", "Detail = cconv(upsampling(Detail,2),reverse(g),2)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Recover the coefficient by summing." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "A = Coarse + Detail" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Assign the result." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "f1[:2**(j+1):,:2**(j+1):] = A" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Write the inverse wavelet transform that computes f1 from the\n", "coefficients fW. Compare f1 with f." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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N3S6tVkvoOVspVFARhgURFo02NjakFS6bzUrP8+joKDqdjmgFslNG\nRSuGvTsjyqBALNBFNOocWQCC2AFg7969EprydaFQSFAcQ1018vH5fKIKQzRVKBR0+Wm+loOS4vG4\nIC72tqtGYV2gi/wYuhLN7tixA7dv3wYAfOxjHwMA4c2qrwN6yNdms8kxm82moDeeW6FQkM9hvhrQ\nT3/jfVSJ0bx3Ksoj8mPBD+gxNd7Ktt35xWIx+Hw+cVB8qFlQiMVikrezWCzI5XK6ogWRFpVfOWyc\n1SaV5Mh2L7fbjWg0ilKphEAgAKvVilAoJMKev/jFLwTV1et1OJ1OXW+kKjrg8Xjg9Xrh8Xjk3JlX\no/hAsVjEzMwM2u02SqWSCA2oQ4wCgQB27typU7pgLy4/h06Yi0LNifB+kH7Dyhur6FR1oUIHK2Bq\n8YW5R5PJpMtNGmbYw2Db7vxCoZD0qwKQiqPNZkOr1cKePXuwuroqxZAjR45gbm4OH/rQh/DGG28g\nn8/DbDbj7t27+PM//3O88MILCIfDuHTpkk52p1arYXV1FW63G319fRIm1ut10cgjUnr55ZdlrCR3\nFRYNmE9jHsXv9+PZZ58V5RnusrlcDn6/H6lUSqcYTREEoLc7NxoN/O7v/q4MGeesD7LoiSCBHidL\nTaaTykMH12w2RTnY5/NB0zTJJdFBl0olnDhxAqurqyIkEY/HhX81NTWF8+fPb+ta+KCZ2sZG5KZ2\nRTC6YW4Y6FJQSA2hUG6hUMBHPvIRAMB///d/A+iiHJUSw02SyIhyZQCkmwmAcAiZUgF6hRX1/YzE\nAEgHFNBDcYFAQNDm448/DgC4cuWKTmqKoIO5ydHRUd2AI27ivHZ1BvdWveVqUUil9PCc2WMP9O49\nnwegm1skn3Ir23bnR4UVoPsluN1uCT8tFgtmZ2cFbVE4gGhsZmYGV69elert4uIiRkZGxCFycbCi\ny8qmw+HAiRMn8MILL+hm9gLQQW2/3y+y+mqOrtFoYGJiQrTE+OWp6hZEo6TY1Ot1EY0kNYXvYU5Q\nPW8iMt4XVRONC0N1gipiVBElq8lEqHT0VqsVKysrsFqtmJqawuzsLLxeLyKRCJrN5ttWxQz71Yzf\njfpQU7hD/Tv7xYHu2uFUN4Zx8Xhc3k+lFuaOaQw32f7m8/nEUbGbCOgVFxwOh1RwubaBntOZmpoS\nQKJqO9J51Wo1CS3p8G7evKmrNrP4cPToUbkelTzPZ00lbm+udKs/swAK9JwfZ9PwnDYPV2cEyXv/\nduT9bXd+zD+xAMHBOmpyn5SUer0uqij79u3Dzp07USqVcPv2bXGYg4ODuHXrloSW6sWqfLvV1VUJ\nnyuVCkZHR6UHkTd7fX0dw8PDACAtYnRWJ06cQCqVkta1oaEhcVbs2QW6owgnJiaEQ8iKrWoMVZnT\n46JjxZeIlFQbtUpMpLlVfoRdHg6HA5lMRu4HK8LVahVmsxnlchnr6+s4ePCgDDlfWVn5tXzfhhn2\nm2rb7vwIj9m4ryYkbTaboCjOBK3Vauh0OojH42i1Wjh+/DgKhQJisRgWFhbQ19eH0dFRHbdNJfya\nTCbRwqPTbbfb8Pv9wleiUykWi1hcXBTZKYqBOhwOhMNhSTqnUins2rVLJx7KfF0ul8O9e/cwMDCA\na9euod1ui74bP4e5Tpo6fUtNRjNMUkUVGCKzUs1rJNpVuWRUeiHCbrVaopvGKXBAjwtm2HszojGu\nWQBCQVKNYw2Abog7NTUFADLU6Cc/+YmEwAwh1W4FtRuIAgjM3wIQIQ3VarWabPYqm4H8uNHRUVFi\nrtVqEnKq7WGPPfaY7ne3bt0SxKVu8Px7s9mU6+SY2s2mtq+pkQ//3dzDzkYGvpfnyWef9QSex2b1\nGtW23fmNjY2J4CdzIxQTYOjLanCz2UQkEkGxWMTy8jJcLpfw1ILBIObn53Hv3j3s2rULU1NTuHnz\nJoBeTyDD083Ow2w248knn8TCwoJQY06dOoWLFy9i165d0hdJ5LiysoJsNouRkRHcvHkTzWYTqVRK\n1FhYcQW6rT3lchmpVEqUW6LRKNLptI4GMzQ0pCO/ckPgPVEXAp0dz52cKiJA/o7/UjORuRF2oly6\ndAnNZhOzs7O6bhOfz4eDBw/i4sWL27QKPpjGsFItHnEjBaAj+XJNulwu2Xz4oE9MTAi/j21malGq\nXq9L6KfmxegA9u7dK2KlS0tLALpOgeuBjAqgJwVFDU3+jsdX6WEkD9PJJ5NJaStT+3iZw1S7uZhr\nV+8D0Nvg1ZBeTemokQ1NdW7cHNQ2O97HXC73m9XextDT4XBIP6rH40EwGBRP7/V6he5CQQOiwE98\n4hMIhUIwm80YGhoSIiMdJh0EE/2s4qpffqfTgd/vF3l8Kp2QK6cKlzKHVqvVMDAwIOiNDpyoT+0+\nqdfrKBQKyOVyOHz4MDwej4gO2O12HDx4UByc6sB4bkAvBFbnpKoOjue31UR6qloznZDJZHD79m0R\nirXZbDIGkcOklpeXf71fvGGG/YbZA+H5hUIhoYAAPXWHWCyGfD4vzi+XywmKoUAj5Z+q1aqQktmi\nRl4Rd1vKQmmahmAwqJt522g0MDAwILkxdRIVeW9qmxLPgXL6iUQChw4dErjP8JNOPZfLodVqiTgD\nHVy5XBaCNID7yMWbickMZdkyR5RINZzNPc+8J+rxmFhmuw/zpWazGf39/TJ/2LD3Zszd9vf3S7jF\nzReAdFioCj4knwMQsVFW8gHodPVU4QuiHxVtES0Gg0GpzDKUnZiY0IklcN2yKux0OiVSymQygujU\nqjXPiRGWz+eTgsyVK1dkDbHCqg4gUsNatUiiRjibOzxUU9v5VNqZqnLE8+T9Zv77reyBtLcxF0VT\nq5Rq+EeHR4Jko9HAj3/8Y51SBFVxs9msoEY1J0D6C/OJlHcvFAoIh8Ow2WzSd0ikxH5jVYElEAjA\n5XIhGAyiWCxKMUMtSKhok4iKqI/GIgQLKjS1qLF5EXDhbF4UfAjU+8Hj8wEym83I5/OyyJnLvHXr\nlqBlw/EZ9jDatju/vr4+ySmwQhsMBrG+vi40kUqlgomJCXFEnFtLx9JoNMQpUdqpUCiIHqDf74fD\n4YDVasXg4KBo4t27d08an+/evSt/K5VKGB8fl1nA/f39suOazWbs2bMHx44dQ7lcxokTJ/D8889L\nL68qNmAymbC6uopsNotkMolIJCIyWwzbn3nmGQQCAV3HhqrSYrFYpDhDPh/QU8Cmk7bb7bqxh2qv\nNB03UUEkEkGtVpNEPGX+6YTT6bR00Rj27k3lrm7O2QI9lDU+Pi6/y2azMkKV8lOqfBnJ9iptIxQK\n6egiQDfVwTGUmUxGp5MH6IcqqciPxwwGg7IGLl++rNPOpKlaeQDwyCOPyBrbfC6Afm6umqrZSsJL\nRbNb5TE3awECXeTJe85ij8VikWe3Uqn8ZhU8SqWSyL5Tx44S8HQAjUZDpNyLxaIMHPL5fPjyl7+M\nf/iHf7jvi9A0TTov1Nm5zB22220cOnRIBhMlk0mMjo7C5/MJp5BoTBUXbbfb+MxnPiODyZkP5DFV\nugv1BZvNJprNJpLJpLTw0GGHQiFkMhlBmSqiU8mxRKysfPNn0llIofF4PLowl06VD4/dbteJOnIy\nHtFurVYThRrD3pttFW75fD4RLuB3y1kqQHdjokDHiRMnAABnz56V74MORZViU0nODG/NZrO0n21s\nbAj/j47E7/frdPBYtPj4xz8OAJJzB4Cf//zn4kAYCqvpFKrD7N69W45Zq9UwPT0tPwM9ShegbzVT\n+/RVdRk6Ot47t9stf1e7m1RGgzrCla9jVKnOCt7Ktr3gEQ6HMTAwgGAwKIl53iSVAa9pGmq1GgKB\ngAzvsdlsePHFF6Uxnw+0ypnjHF+GuJVKRcK+ffv2YXh4WMY5sqk/HA7j7t27gkbdbrcsur6+Phw4\ncEBUZur1uhRc6NTo+KrVKkqlEqxWK/r6+kRVmvxF9hPncjmR2ld3P7WLQw27N2sBcvYwiyHkBXKh\nqO1vbP3jQCUKOqgLkzxAwwx7mGzbkZ/f78eRI0dkZsXc3BwqlQpu3rypk+opl8vYsWOH8Nr8fj/i\n8TgymYxuh1D7Zmu1GqamppBMJlEsFuHxeERCy+l0otFo4MCBA1KwIHIKh8PYs2cPksmk7N783C9/\n+cvCmSM0p1gAizYUHGW+0ufzyTWSolCr1USdhny+Wq0mbWmAvu92M++JzrDT6Uj1W+3KoKPcvIls\n1pWjZqFKwSBaNuy9GRP9jzzyiKyj5eVl6avmZp3P5zExMQGgu/Hw9wxb1RwxN8RqtYr+/n4AEP4p\n0EM84XAYTzzxBADgzJkz8t3yc4AeomIkBQC//du/DUA/7Mflckk3B1/X6XSEkkP6zdDQkITqw8PD\n2PFLmTfyCT0ejy6E3dyjvjmPzeeaCFMtiPA9akpALRzxOdrY2NB9DhWOtjLTW/7l12R/9Vd/pY2M\njEinB9D9YpeXlwUd0al4vV5xcLlcThr4C4WCzKlwOBzw+/1Cm2HlkuorZrNZ5LCDwaAIEHg8Hly4\ncAH5fB7Hjh1DKBTCysoKLl++jGq1ipMnT+pCAaKtcrkMt9uNl156CaFQCI8//jgajYaOUrJnzx7p\nJ47H49IHTMn8er2Oer2uq9oy/GduD4CgOdUREs2x8kxorxKdKXBKDmI+n5cKdLvdlrxoqVTSFZ5e\neeWVbV8PHyT74he/qAHAwYMH5Xfr6+vSX8sNRu3DVdvS+Hd1jjIfajXXpYbVdLg+n09+bjabQuCn\nw9y7dy9+8pOfyLEYFvNfVX1GzfmR2NxoNKRazXY8kvr5szqOk9eh5ibVMQwA7qNxcY0zpFdFWXkc\nVfxDVSOiuk0ikZC/Z7NZ+fvly5fvW9vbjvx27NiBoaEhpNNpcWAWiwU+n08GiTPkbDabePzxx3Hj\nxg3RveM8j1arhUKhIGom4XAY1WpVEBGrnNFoVEJiNYfGAeJEZtT8oxElARBnwrxdOByG0+lENptF\nPp/XDVQHeoosqtCC+kWTgsPQmSrMZnN3psZmBMjcCOk7aoGFaBDosd/5ehK9S6WSCDlkMhmMjIzI\nXJBOp4NsNiv5GsMMe1jsgUhaEYnVajUdQRnoqUvQEfh8Phw+fBipVEoI0evr6yLlzbkazHFFo1Fc\nvXoVuVwO0WhUJKZIPia7nlVVq9WKZDKJkZERHZKqVCqi+8eqFcNN8gaXlpZQLpdluDJ5huQhMllM\neola/SJ7nVQVhqFsBud5MlGsvhfoVc+Y7yN3cXMRhWkEs9ks0+CSyaRIiHM28FaqGoa9M2MHhNvt\nlva0RqMhHQ9q3paIbnR0VEJMbmqJREJUStTKKRHN+vq6TvUZ6AIFVj4HBgYEkbEKqiJ8VcGFn80i\nGo/J4gnRqDq7Wh0+TkSmVrX5LFssFkFeyWRSzp+frW7cKt9VLQDSVFI//85oSb137Az7VWzbnV8i\nkUC5XJabpXLYKBvFvNqBAwcwMDCAaDSKa9euIRaLodlsysQxdnOoD77JZMJTTz2F9fV1XL9+XQjT\nQPcGcVwj0KuA0ZGqahcMS3mODBHpGP1+P0wmkwydJrKkLBW/DNJVWMTgfwxn1YXECiyd9FYkTTX3\nAUBX9CEypQo0uZPcOKzW7kB05kXS6TRKpRKGhoZ+5QVjmGEfFNt25+d0OrG2tiZjKw8cOIBbt25J\nDoToq9ls4tatW1hfXxfUxuLExz72MeRyOcnPsSd4Y2MDqVRKOH1jY2O4du0aDh8+LGEguyyI+ug0\nbt++jcHBQdmBVldX4ff7dSV2OsFisYhgMAiXy4W5uTn09/ej3W6jUCjA5/Mhn8/LLGGeO9Abgr65\noKESsBkCFwoFGcdJKg75i0SCdMyq06bz0zRNXjs6OipIdH19HR6PB+l0Gi6XC/39/bDb7di5cyd+\n9KMfbfdy+EAZ6SE///nPZdNSWxf5HdntdsnF7dy5U/pTiaLsdrt0URC5uVwuyaWNj49L7y6RFQU8\nAL3mHYsU6uamNhmoiuXq+XHzZi6NVC+gx2fczNPbPICIlDAaz2+r7hcVearIjyiRCFQl5VNhCeh1\nuuRyOd2gp7creGy785ufn0en00FfXx/i8TiuXr0qIqAkNbNKlMvlhKcXjUZluM/58+eFAwhAkvf9\n/f1wu91YWVkRB9Df34+VlRWZk6qSiz0ej8DxjY0NyQ8yJGUrnOqotvo3nU4L7485SBZfNpM06USJ\ndjdrCzKhy7zi3bt3USwW0el0h52Pj49LFZkLhg4Q6C5yNRxhH7XdbkepVJLKLsP8ZDIp992w92Zc\nE2oV3ul06iYTAl3unDrkhw6A79+xY4fwAFUxTjqSq1evStjMZyAUCsn7VeECOj1VuadYLEo6hOtS\nzXer64nXokrFbSZg0zY7LzVNw/EM6rGSyaQUUex2uyjM0OGxGwvokbUbjYa832QyycZBh6xOIfR4\nPJKK2Mq23fmR+EudvXq9LmRb9i+SgsJFQ11+FkcWFxfRarVkChXDw09+8pN444030G53RzPGYjF0\nOh0sLS1hfHxc2r02K0Vw16TzUXMRm50VoFd5NplMiMVimJ6eFmQHQFr1eCz+tzmPoe7IqvYfFxIF\nSXmtJE0zb0pnSWoOz1ndfdXPdzqdgkZDoRCKxSJyuZyoeBhm2MNiD6S3N5PJyO7EORPU3iJFZffu\n3ajX68jlcmg0Gkin07DZbHC5XLqOBlY26/U6Ll++jEQiIbSPfD4vw4sWFhawZ88e4cGZzWZp7yIH\nkHmyzQlXdSek45iamsL169ehaZo4FAovqJVeFjNUHp567M05QJWsTRkgh8OBQCCg60XmnOFWqyUz\nV1l1Zl8vizbM9xFFDw8PI5FI4Pbt2wiFQrJ7GvbejMo48/PzOj08brLcYAYGBqSVbHl5WdYW38NN\nG+ghnnA4LIWTmZkZobLwM5vNpi7U3qxgnEgk3pJfx99xwx0cHJRiHdGdukZ4HLI1aFs9N1vRWtQ0\nkDqzZnMbYD6fl3tGRMcIiMdU5a2AblPCVgh8K9t258fZEZvFDVWtMXLmqNDi9XrxW7/1W0IYJfeP\n4TErUVeuXIHZbMbk5CRarRb8fj9Onz4tSX8KeTJHFovFEI1Gsbi4CL/fD7/fj/3798ukK1aW6BAZ\nEk9MTODixYvwer3IZrMIBALI5/OCYH0+H3K5nK5dTV0EKgKks2MXi8rxcrlc2LNnj1SniSxJkGZP\nMtDNbySTSRkLkEgkhOsXDofRaDR0k7QGBgYwPj4u/EMKahr27o35pTt37uim9NEpMX+XyWTEqXQ6\nHVFGYeWV1Cqg91zE43FpSWOFF+jN6FhaWhJ+odoTTueQTqclz6iCh60ENdS1wuOoAqdcn8xf8zo2\nh156WlQAACAASURBVLsqkZ7NBvwZ6Do8EqZVkVLeB5XMzdxjMBiU46ianSoZm/env79frnkr23bn\nR+UVcu3oDNQ+POrn0ak1m028+uqrEvay1Y05M6KdcrmMYDAoHLZqtYrdu3fj5Zdfht1uRzweFx4d\nicUUSuDAIfL+eNP5Wjo+k8mEeDwuWoIXL17U7ZpAN3+RyWTEYQG98HlzjyORYbPZlAXkdruF96jm\n4jqdDnK5HBKJhBReiGB5LZTS4nURcTocDlGJVmec2O12HD161OjwMOyhs213ftwJOOeWunxqXo19\nspxOVq/Xsb6+LqEbHQPfMzQ0BIfDgXg8LqMbGdpGIhFEIhFkMhncvXsXH/7wh8XR8DV0BnSCu3fv\nxvLysg5VAr3kcLPZRCgUEsl7IkOSqHlNqlz95lBDLaKoXRyhUEiECIg8eexmsylUIRZjCoUCQqGQ\n3Bd2clC/0OFwSHsfW9z4u76+PmQyGalKG/bejMgpFAoJ8uMQLUCP/qmwzE1p8/u5+aozZWgej0cQ\nIQsjc3NzEgVQrAPordl6va7rjFCLBjy+2s1E5KfyBPkeIi+bzaabWLdZuIBrlu/h9REhqzSuRqMh\nbXH812w2y/UT2a2vr8u1qcUknpuqkm21Wt82pbPtzo/VrVQqpXNAmwcpM5fHkZakpNAR8As2m80i\nEEDHUygUhKBsMpmwZ88enDt3Dul0GmtraxgYGJAeQY/Hg8HBQWQyGayvr0sXBfNkVFymUCkXCB0M\nFyIdEqvEFGZQSaDqzA3VqfE/q9Wquy6V/8iwgeEJS/6lUklyIJQan52d1YlDspBCh0onHw6HMTEx\ngVQqZTg/wx4623bnNzg4KKgjFApJ/E8lllKphGQyKaEgANHCY0dEu92dk+vz+VCpVATNsJxeLpdR\nLpcxOTmJUqkEt9uN48eP4/z583j99dcxOTmJmZkZqSDv2LEDqVRKWt76+/vFoTJ05XQ5Fja4mw8P\nD8PtdotzpBPWNE1oLyr/iQRo1emxK4Sy+KrUjxqOOhwODA4OQtM01Ot1VCoV3L59G+VyGdPT08IV\nHBkZQTqdRjwex9zcHI4dOwaHwyHCC6r8Ph2tKrBg2LszIhkqhgMQaTag912qm7zKlVMH/5DiwvyX\nWjiJx+OS19q5cyeAbuGD3MCjR48K+uFckdu3b0uRRD0HtbDC8+dERaDXtZJMJuU9RHsce8pz3ixC\nwKIdAGlMAHoIl4CGx9wsUlAulyXPyWJPKBSSIg9VytXrAHp50h07drxt59K2Oz/eMAob+P1+dDod\nKTgwh3fhwgW5MZ/5zGfwwx/+UJCfSlAG9AOKSB8hJFaVVviwr6ysYHx8XFBlpVKB1+tFtVqVgkup\nVNpysaqV31arJbOFCbfZpcIvlvlIoi/+zNyf3++H2+2WIowaHqvjM+kUKT9FqSyTySRKN6xWU90a\ngMwSYdigEqTL5bKEBpsnjBn2zo0h6NjYmE47j9+n2lJGjb/x8XFxSqp2HR0AHY3b7da1x9HoEEdH\nR0UVZmNjQ0JLtepMR8RUEtBz2Iya+DPPmQWFXC53HyeQghk8J/VnXgffT24qAN36pnOiDBzQqzAX\nCgWR4aez9/v9cu7UFQR66jUqlY1sh7eybdfz4zg7r9cru4Xf75dQrlQqIZfL4dFHH8XBgwcxMjKC\nH/zgBxICcwe0Wq3I5XLSmkauGwCdxh2/XIag/O/atWsAul808xF8HzX51Dwkq9Os6PILqNVqSKfT\nGBgY0C0AAEKlYe5DRX4qj08dmERTxQs2F2hY7SVDns6aTpX3khL6t27dQiwWEykrzjWheIPdbpcO\nG8MMe1jsgcztZcLVbrcLMvF6vVhdXRVuGx9mzszduXMn7ty5IxVMOkyqtKiqyhRGoKYfK59DQ0OS\na+ROxoJGNBpFsVgU4vDQ0NB9BQqaisYYds/MzEhfryrOuhXs5t8CgYCgRO5WW3WTqGq0bM1jiK9q\nGtJ5k+fInudYLIZSqYT9+/djfHxc5rayI8XhcGw5Bc6wd2ZEWVQAArqFAv6eyMput2NychJAl4JC\nWSl2YahSTQwR1bXEFAzQCzFHRkbk/Xfv3hXkyL8zyuHnc3NVqVj8HdcR0KOYOJ1OQWTMMVer1ftI\n/UBv3aqScKqpBSA1J85r4jmp3RqMwrxer6DJZDKJs2fP6v4+MTGh00BkwWQr23bnp87lfeyxx1Cr\n1XDnzh088sgjWF9fR71eh9frhcvlkv7FyclJgb9Op1P0+4Be2wy7QlikqNVq2L17NwqFgqhBT05O\nSqWzVqvh5s2b2LNnj/Dn2u3uaEeSK6vVKnw+n9xYtUuDYS1VZZLJpE5sgKEloC92cNYoH5C//Mu/\nBNCdfvWTn/xE3qcWPYCePLfVahXJfW4AACRdoP5M0dRKpYJisYj5+Xl88pOfRCQSgdlsxtTUlOgO\nGvbeTb3/5E2ura1JFZYtbarwhdvtvq9iyco8j8X30IkyXQT0wuJ6vS7E6UQiIc8OtfeoogToxyWo\nGnuqth4dmcpWUKMR9W80nivPbXJyEh/+8IcBAD/96U9l3gzfr0Y86qB3XidpaXwtjT83m00hMp85\ncwZAN0XG+zg1NfW2w7m2fdXTgeTzeSwuLsqoymq1KsIFkUgErVYLzzzzDEZGRrBnzx4cOnQIkUhE\nWrzoBOhMmYujM9Q0TQRQOduj0Wjg4MGD2LVrF3w+H1KpFEqlEhqNBur1urTb2e12JBIJ+SxAj/wA\nPRrrdDqoVCpSlSZ6o9NTf/b5fBJ2suKcSCRQr9fx9NNPY2xsTOguaueIOtvDZrNJrpFFIBW5sdJL\nlNzX1ydhPRcY85SqFJFhhj1Mtu3Ijzm/QCAgOT+v14v5+XmYTCZEIhEsLy/r8mXs6pienpbeYL/f\nL9JSZJp3Oh0dbzCbzYpKDIm/Tz/9NObm5rCwsAC/349r167hU5/6FD760Y/i3//930VggZ0We/bs\nwfLysjgJVWiUCItTpFhcocoy0NulmHOkcEOpVILNZsOrr76KcrmMu3fv4rHHHhNeEkNWtUWOaI7n\nwX9pmx00238CgQCsVitWVlZw7949ETVQhyhtfq9h79yIjFSFbI/HIzL2XBOcXQNANjEAwv2r1+u6\nAVQAdN91p9ORKqjaifH0008DAC5duiRDkRjqPvnkk3jxxRfl/NTKNKBnFQC9zZ1/J3ke6K0ztlrS\nWJTgmg8EAlLYmZqakhB0ZWUFAGQELI/J96nRzObzUTfqTqcjqJpIlxoBAAQ8vJU9EEmrSCQi0J4t\nXP/xH/8Bn8+Hubk52Gw2rK2tIRaLCQpSEV6n00E8Hpc8CB2SOrGNiIk5QdqZM2cQjUYRCARkstad\nO3cwMzMDl8uFUqkk58cWOHaTqDCfoSkXaaFQEDRHqgqLK+QaxmIxHDlyBPv27cPFixcRCARkcR0+\nfFicJikyqsw9oM8Bbv5SWRRRRRvU7o/h4WFks1msrKyg0+lIz+/m3I9hhj0stu3Oz+FwYGRkRGZv\naJomnQblchn9/f1wOp04cuQIcrmc5PJI0rXb7ajX6wgEAqJLR94cAJnzS9qBymszm81YW1tDtVpF\nJBJBPp+H0+lEPB7H888/j0gkgr1792JjYwM+n09azTKZjFANVAeYzWZ1GmgUESWJ2GTqzko4evQo\n7HY7HA4H6vU64vE4otGo5FFI1K7X67hx44bwD5nLBPTOTS24ANChUho7Vlgdd7vdmJmZwd27d8XB\nq2hvc/7GsHduvJ8+n0+S8hMTE/jxj38MQJ/AJ3Lzer06LUYA0toJ9FCQyhdUNfKIMC0Wi/D8fD6f\n5PqYKx8fH5eKvjqsSEVx6oa6GQlubsvkv8eOHZPrIJokGt3MvdssgaV2v3BNA2+P+NR1T6AAQOSw\nFhYWZJwngC0LjrRtd35utxvZbFb6e30+n3D2qtUqcrkchoaGhJumaZqMXqR4gMPhEAFTUjU4/0Mt\nTpDPRBTEMJWik6FQSAQCisUinnjiCdhsNmn3qlQqiMfj8Pv9UgGj82k2m+jv75f+ZJvNJtqAqorH\n4cOHhZenzt9oNBowm83IZrOIxWKIxWJ47LHHxJEx7OXnMiHNMEhFg0Sh6uJVQ2UWW8LhsBRLqJ7D\n1xr23o33MxqNiqPp6+uTFjF1aDkfWpPJJN8pK7zqnGW+F4CO8EsHyJy0qpenVphpV69eFU3Lubm5\n+wQ31JwxN30eC+hNFgR6UcKRI0eERE1nD/SKMOogJbWwwwoyO5Z4H3j+qvPjmlYLQDwndb3zPNLp\ntO6a3m5tb3vBgyfOwkK9XsfCwoI86MViEdlsVk6cw8prtZpQOD7/+c9L0p8jMDkLw2KxSG8knZxK\nHiV9hu1hKrN8fn5eN1CasliRSAQ7d+4Ux8aiQygUwr59+5BOp4W0TWqNxWLRzWbgfI5yuYxqtQqH\nw4FUKoU333wTq6uraLfbuHTpkuQva7Ua8vm8ru9ZFVdQiyqbq8pms1kWmlpZczqdGBgYQCAQkN5f\nOk2j4mvYw2bbjvyorsrkv81mw4ULF3QKxHQadH5UWmFO7Lvf/S5arZbwAtmIzd5Wzvfw+/2YnJzE\nwsKCIEbuYMyHDQ8PIxaLod1u49q1a/D5fNLry91zZWVFnAzzfyaTSYaPE0nR8dLpqlwvcgBNJhPm\n5+dFRYZ5SbUqzMl0KiGZVd3NIRL/3czTI/lbNaK/Rx99FJFIRFD4Znkxw96d8btRO2Zu3rwpSIfG\nVkYAErEA0EUM3LxU7hvDSc6RBnqtXGwPBSApJaDXHqe2xHm9XkGU6uAftb1uM/JsNBryfoIFiuoC\nenVo/js7Oys/M/+tHrNer+s6TDariTOiAqBDher94u9Vkv7evXvlPrzdut5251epVDA3Nwev14t9\n+/ZhcnISP/7xjxEKhYT/ZLPZMDIyIqGkz+cTifl8Po9Go4FoNCq9rOxlrNfrmJ6extLSkogUcB4w\ncxr8sqlwwmHLly9fhslkwuXLl2V4EkUl8/k81tbWpEVORVrMrXCMZqFQEDWXvr4+nD59WhSk/X4/\nIpEITCaTKMKoYzqBbkjAyhfJy0CP4gLcL7KqTqSj5BbHd9LYEhgM/n/tnWlsW+eZ7/8StVMiKUqi\ndlu2LFmWk9hOvKVN3YyTLuiKfEnS6Uxa9Eu/z2Du/TjADHBxUbT34t6ZXhSdwUwv0AK9A9QtOg2C\nJM1SpLHjxHbiTVa8xJYsiVqolaQWUsv9wD6P/uc1jxonKZ2Gzw8w8obSIQ+pw/c86/+JoLGxUev/\nRDnD2ts+POK+Xr16VTX6lpeXNYMv7uDCwoJHP1EKkmWj4o3ugQceAADVqQRydXzi7kphM8fM+LoR\nvbyBgQFcvXoVANDT06PPLzfqcDisLiJfa1I7yK1ssoldv35df0+qKuT8gE3jBchtmLIRco0hl165\nN3Z5L/K7cm48A4RVawDg6NGj6oJ/7IqcpSh47969+Ou//muMjY0hGo0iHo9rj+3a2homJycRiUSw\nurqKlpYWDA0NYXV1FfX19ZrUEIvl0qVLqK+v1+LkaDSK9vZ2nDhxwjN+EtjM0gKbYowLCws4fvy4\nBqbT6TTee+89jUcGAgHMzc3pbF/p4jh48CAaGxt1xga7ojJrYGRkBA8//DD27NmDgYEB3LhxA9PT\n07rBiSvNQ5llrCbXA0pNH8OvyXdBiYfK++SBL2VlZTh48KAmiurq6rRn2DCKiYJvfmJ9fOc730F1\ndTUuXbqkQ77X19fVnBcLr6+vD9PT02hoaPDogM3Pz+PGjRuoqKhAPB7XiVWXL19GTU0N2tvbNdbW\n1NSE2dlZLC0toaysDOPj43q3XV9fRyQS8TSOl5WVYWJiQtVaqqurPUougUAAjY2NmJqaQjKZ1Er0\nuro6zbCKvFV5eTkGBgYQDodRX1+Ps2fP3mHFiRstyQ2x5GSzkiwyb3ZyjLSmcaW+JDoElvsWwQeR\nwgoEAhgcHDRVl48Acb1aWlrwrW99CwDwox/9yNPCBeT+RuIKi+o4AM/g+Hg8DmCz9i8Wi+ks4Pb2\ndk0kiAWXTCY9wgJyw5MsaHd3twofDA8Pa4JArNXx8XH9ftXU1NxhMc3NzakrzjF06VrZu3cvLly4\nAGAzccPJPzkvwBuike+BK9oLeEVE5OczMzOe8a1uGVhdXZ2KHPyxGb4F3/wuX76MRCKBn//856ir\nq8Pp06dx+fJlNeNlMHl9fb027Pf39+PixYuIxWLapysTySRGJu0xMsVtYmICU1NTqK+vV/N4dnZW\nL5bl5WX09PQgnU5jdnYWJ0+eRCQS0RiiCCdIfGZ5eRmTk5MqNTQxMYFwOIz29nakUinNLotFKhuv\nZHlPnjyJXbt2obOzE5OTk5qYkE1tcXHRMz9Y/nASp5QLQr5AoiAjmW5xIaampjQu6SZEJEwgQg4j\nIyNIJpOe1iLDKBYKvvnJF+7EiRMAcr760tKSusOCxAckplFaWorBwUGdZl9aWoru7m7Mz8/rl1o0\n69555x10dHRgfHwciUQCDQ0NaG1t1SD/4uKiysFns1l1Y8UqBXJ3tZ6eHoyPj6OmpgapVEpFBaR9\nbHl5GUNDQ5pMkU0kFoupOk1FRQXm5ubQ3t6upTriuos7vrKyor2bktGtqqpCU1OTdppwV4ecQ39/\nP7q6ulSS/tq1a3fo9YkVKB0dhw8fRjAYxI0bNxAIBPD6668jm81qjMr44Lz88ssAcjfGv//7vweQ\nqyDgmSwANCEnj7mF5vPz83qMWFEcuA+Hw2oFShKCLSfxTIBNVeSqqiqNPWazWS2bkes9lUp5ZmzI\ncfK8klgBvDJbYqHGYjGdl8FKz/I+5aYMwHMzZiuQlc3l3CTmKM85PDzseR6x/CRs093drc9z5syZ\nO5JNzD1RdQGgPbXS9iW6Z4uLi9qQLxvBtWvXUFFRgfr6etTX16O3txfZbBaPPPIIXnzxRS17Eamp\n7du3Y2xsTDPIAFRMIZFIYH5+Xt3D5uZmxGIx1RTcvXs3gsEghoaGkM1msX37dhUmFcFTYDNhsrKy\ngh07dmBxcVH7e2dmZjSjVlNTo+rS4l4/9dRTiMfjOHfunErv8x8yGAziwQcfxOTkpMr3c3avuroa\n3d3d6Ozs9BRDLy0toaKiwqN6La6B9ELLtLza2lqcPHkS27Ztw9mzZ//opCvj/bO0tKQuINfcyRfY\n3dxkA2KrvqurC8Cm+8vGwenTpzWpIEZCY2OjbiRShQBs1r9lMhkcOHAAAPT7BXiHfcsxcm0D+d1S\nbtOTzG0ikdDN/XOf+xyAnFiHnKeEcQDooKWFhQVNuEiYCNgUaO3v79fXEgk60b6U9yHI+4hGo3ot\nj4+P6+eXj3tS5Cx9gvIFlTcUCAT0whAhULHm7rvvPmxsbI6JLC8vxwsvvIBwOIxAIIDp6Wkd4Tg1\nNYV0Oq2N/CJtVVNTg/n5eXUrt23bhp07d6pVJxddJBJBJpNRsU+xvLiIeWFhAcFgEN3d3YhGo1hZ\nWUFzczNOnz6td2M5T1FkmZubQ1lZGU6dOoW2tjYtc+CZB9XV1aitrcXx48cxOTmJn/3sZygpKcGD\nDz4IIFfE2dXVhXA4rCoxQK4cRy4gyS6LnL58qRoaGlSthgefNzU1eYZaG0YxUPDNr+sP0tKizRcM\nBpFMJnXMotw9JJ4n82hnZmb0v+JyykhGcaV3796N27dve8o6ZCD33NwcDhw4gB07duDs2bM4evQo\nNjY2MDIygnA4rBbn5cuXNc4mm7QMC2ppaUE8HtfymfHxcYyOjqKvrw8tLS2oqKhAKBTSMptoNIra\n2lrd4GXY0NDQEEZGRlQ4Qcb2SWnP8vIyfvjDH+rG9fjjj+P+++/H2NiY3imFq1evYmhoyCNkKpua\nxPdqamoQCoXQ39+vCjHZbBaRSAQDAwM6AsD4cMi1KwklAJ5EEtfHiUWTyWTUapHavGw2q4IAcgzf\nJMfGxtSjkfKY7u5uz2tKwz/XAYorXFFR4RkfIf+V8xdrDYCW5HR2duLcuXMANpMs2WxWkzyJRELd\nXrG22tvbPaUq4oJymY3E0A8fPqzJE05syucg5yQNDfI5ymcimogcOuPumHzcE7c3HA6jpaUF8/Pz\n2mAv7VtiaXFB78rKCmZnZ1FaWopoNKqDvKWfNhqNYnl5GRMTE6iurkZzc7PGE3p6etDS0oLBwUHM\nzc1pP29lZSUOHDiAbDaLN954A1VVVdi9ezcqKir0QpMpcEDOLZientYLa2xsTLPA165dQyaTwbZt\n27B3714MDw+rMKpkVVdWVhCNRjXZEQ6HUVNTg9HRUX0/0nImGeZQKKSlKFeuXPFkeSXhkUgktG1O\ndAS5uLOkpERFHMQi5D5NkRNzh1wbd4/Ul3V1dWlmlRVzWOlHbjZlZWW6WUjva3V1tW4KsmEMDw+r\nRxGLxXSmhWxuyWRSvy8dHR04cuQIgM25vmVlZep2y4RDYLOImif4SWsnkHNdgVy9IbfHAdAeewBa\nmA9sbshchSANBfyeIpGIuvc1NTWamRZvZnJyEoODg/o5At6xAFw1Ie49C7FKfNyPe1LkXF1djaam\nJrX6xOqRWBW/wWw2qz2A0pwdDAbR0tKig5yDwSB27NiBtrY2Le6VGjkpG+nq6sLFixf1ThcMBtHb\n24vXXnsNO3bsUOtuZmZG53hUVVXh3XffxfT0tOrixeNxtLe3o7OzE+Pj45qkkFm67e3tWF9fR1tb\nmxaGSq2hDCsSl1rmlkiZi8hXcQJHSnDS6bSWtZSUlCCVSuHGjRuorKzUY2VTZCuusrISjY2NOh9F\nPlPpTJGsrxU5G8XGPZG0Evd2ZWUFk5OTqugidXiyGbL4pggSNDY2alBzeXkZkUhEC4Dlix8IBLC4\nuIje3l4kEgksLy9jbGwMDz30EDKZjErZX7lyBWVlZaiursbS0pKa2NIqNzAwgOvXr6O+vh7pdBqx\nWAyNjY2avOAC57q6OqytrenPZEMSYda6ujrMz8+ju7sb6XQaMzMzmJubQ319vWZ3Je7J0lSiqssZ\n3NHRUYyOjmonQE1NjSaHpDaqurraM89D3K+1tTVMTU1hdXUV09PTWFhYQHNzs4kbfATItdrS0qIK\nLsPDw5qsks9YJMsAaPIN2JxQtn37dk0+iLXX0NDgcaslcysW0dTUlEfdXF5fat6SyaRaZqWlpZrN\nFSuuurpar5GGhgbPBDUg180hVp64t1x4v7i4qNYqz+plwQOxyHjmsLiwS0tL+lxiNScSCY96tZy7\nPE9dXZ1+PvI6HHJYXl7W889HwTe/VCqF6upqjI2NoaWlBY2NjWhubsYbb7yhsTYxoaPRqL55qZfr\n6OjQtPy2bdtQXV2t8UApK9nY2EBTUxNqamoQi8Xwy1/+Eh0dHVhYWEBPTw+OHj2K8vJyTExMYGVl\nxTMvYXx8HOfPn0dnZycqKysRiUSwtLSESCSChoYGrK+vIxwOazxN3FKxHAFoskaysPIeQqEQZmZm\nUFpaqkrNADx1fPLHFRdJBhUtLCwgk8lgdnbWUywqG2xFRYVayJKUicViuiEGg0Fdz8/PY2xsTAc1\njY6OqqtifHCkfIQHZ7e3t6uwqHzRU6mUJ2MqX1aJ+WUyGd3c5LoIBoOeGJbEuKS8JhQKqVva09Oj\nriX35spj8XhcvQN5fvEOAOigLGCzcJszq1yEzK58vpIezmBzKxwAnSUD5DK/cg3K5yENCAy/ZmNj\n4x3Z6Gw2q2KpmUxmy7hfwTc/qffZtWsX0um0upo9PT0YHR3VcpGamhrtmJCdvqWlRa1D6UUcHR3F\n/Pw8duzYgVAohGg0iuvXr2N+fh5zc3MYHh7GxsYGIpEIPv/5z2N1dVXjcRK3k7jM4uIiUqmUWkrh\ncBitra2etjKJxckfdnZ2VhvNpQtEWuii0agWSodCIVVqEbdcLD5poZP/l9nFMohJzotjfqLyItlk\n/sLJ5DZRmJbX4to/acGrrKxUdW3DKCYKvvlJJnJlZQX79u3DqVOndBan1P1JLZtsjuXl5dizZw8a\nGxs1BihlMouLi+jo6NC6umw2i6985Svo7e3Fv/7rv6K1tRUPPPAAIpEIbt++rfWFUrsnVt3g4CDG\nx8fR19eHvr4+1NfXY2JiQtvugNxd0B2q0tzcjHQ6re1FMv2NRUfFDZcEinwGLEUvG2AqlcLk5CQq\nKiqQTqc1o8WWofxXLAlu9wFyd0S5O0rxtrymbJhSqjM7O4tQKGSW30eAZCu3b9+uxblSDQAAly5d\nAoA7LHtJBEgWNJPJqPUjllNtba26sp///Oe17m3//v0AgN7eXo1nz87OavJELKKLFy/q8f39/fq8\ncp4lJSVq+UlPO7BZXD0xMXGHyADrU3JtYL7EjiQHgc3MrVQ58OsAd87H4ecEoJ8Xt89xu6gkcUpK\nSjwCsi73ZGh5U1MT5ubm8Morr6C/v19VWKStTJIeUvcGAEeOHEE6nUYikVDrZW1tDel0GgMDAxga\nGkJrayva2tq0mPjJJ5/ErVu3VMGZq9gl9iWblbjIjY2NCIfDuO+++1BXV6c9lLIJyzxgmYAlm5hk\nWKXWTuJtMg3O3fQAbyZQipWl7IeTIAD0+PX1dX1+yaaJCy6xQrmIudtD/r+0tFStz8nJSbVi3RIa\nw/ikU/DNb2FhQV2uQCCAF154QSvFS0tzQ7gzmQzq6+vR3t6Ow4cPo7KyUjcvIJcqX1hYwJ49e7Q0\npbOzE/v379e+3rNnz6K7uxtDQ0NYX1/XDGdFRQWWl5dRW1urgVvJiEpyQEpLstksmpubUVJSooFp\n0d+T2MPS0hICgYC6yTMzM56ZquLKipsqWVap4ZOYimgbSqJHMtXPPvss9u3bh46ODt3wZNZwWVmZ\n9i4DuTuhyInL/GPZgEUxWLLPoVAIgUAA8XhcpfyND4ckF3ho0fLyst5A+UYnFtGBAwfUkhHLcXJy\n0mPFyc++8pWvAMhZSdKtIYmLmZkZ/X5kMhlNbkgSQqobgFy8UM5FXhPYtK7Y0xDLKhQKafxMdVny\nZwAAIABJREFUEhosnSXVDAxLVrHKurwOy+mLUSHPC2z2+ct7AnJWn9zcZZSrnLM8t5xHMpnU381H\nwTc/qZUTIVIgl/WRlrDy8nJ0dHQgmUyqMsuNGzfQ1tamJSeidPzd734X8/Pzmh1aW1tDPB7XP874\n+Li6jaKWXFVVperQ8keWxERlZaW6tSIzL1aW9O7KzwKBgEeMMZvN6u8BULecZyVILFASFWw9cm2S\nuBMyI0E2Tx6OJOdWUlKCdDqtGXRRyJHf5wlW4mJLciiRSCAWi+Hq1atm+X0ESE1ab28vhoeHAUBF\nMYDNjai0tFRd4Z6eHnXZ5AY0MzODp59+GoBXpl5ulPF4XL/0kmQZHR3Vx5qamlSNXK6rvXv3evrW\n5Tsi58SJAVYwkueUGyifkztcSzYdufmLFwNAWyvl/QO5G4O452JkyHPJMSy2CkDn/shn6yZReKZx\nMpnUm1A+Cr75zc7OYnR0FCsrKyoIICrNojRcWVmJWCyGnTt3IpPJoKurC8lkUlVcW1tbsXfvXrz5\n5pvagra8vKwaemI5JZNJ/UMmEgl0dHToGMeVlRUtOSgrK9NODCkrkc1DVJjFYhSrS6wwccF5uIu0\n5bk6guI6y3NvbGxosTbgjXVItlhiMhJHlAtM3GfZVCUzLe+f4x1yUQG5C07Ge8rw9+HhYevtNYqO\ngm9+rDfX0NCg8tuVlZUa79u7dy+OHTuGxcVFldSWSnMpjRH3eHZ2VpvHxQyXFHc0GlUXRDYvfq1w\nOIxMJqPDkqSgWGJzmUxGB55Lby6wGegtKytThRVxicVi4wSFKzrK0vNSVsAbFCNJCtaCkwSGbN6S\n1JCsrswSkRKXbDarwgzT09MYGRlBNBrVzVPcJePDIS5kVVWVZs8bGhruKFt58sknPTcmKYURK+bL\nX/6yXiPyPIuLi55BSFIrJxb7wsKChnGAzUlx4i6yIADXyrFaC1t/YqWx4oys5WbNFiS78vI+xAiQ\n1xTkWo5EImqlcTeGHB8KhfTalM+QS2qkv53PMx6Pe0puZHpdPgq++fX19aG1tVXVRVKpFG7fvq2S\n8YFAAIcOHcKZM2cwMTGB5uZm3aiAnJ8vX+JUKqWbydLSEqampjA3N4dMJoOmpiYsLCzoLI/29nYt\nipYpaKlUSocm1dXVIRqNakJECk05oypDmuUD55IR2QS5GFN+h0fycVlLvg3PlfBmQUcp/g4Ggx4L\nluWuZB0IBNDS0oLS0lKMj49jdnYWExMTOH/+PF566SW1+kQNh1/X+GBIT+q2bdv0GhkdHVV3Vj7j\nUCikbWeRSMSj5gPkNiFxZ3nzkc01m83qpiHXp9zQAe+kNXErW1pa9Jxqa2v1NeUalOtezlOOl42E\nY3p8I+Y4HW96ch6MO3eGlYzkuwRsFlFL4T/grQ0UF7ilpUWrFKRF8MyZMzrCU659Pwq++W3btg2V\nlZVqLUns79ChQ9qCJWMq6+vr8dBDD2FgYEBdXtG3kyRDaWlu5q3EGYLBoM7IlQSKxA5mZ2c1+SEN\n/9lsFjMzM6irq0MsFtM/3MLCgl4Q0mUhP5M/nsQF+aKQzUrcVrESxeqTx/nicocPCfJ88l8g92WJ\nRCIedWAONLMFmE6ndTZqOBzGf/7nf+Kdd95BIBBQyTC5kx46dAgvvvjiR/q3NoyPM/dE0kq6HkQL\n79ChQ+jp6dHWFNm4AoEAxsfHVVQAyH3Zg8EggsGg1s5JIkIsNxGLlGynDBHv7OzE6uoqQqGQFjlL\nBlgGIIv1mclkVPFYMrV8dxKri11SjscBm5aeBIZZdpuVmGVz4zsuu9+SOJGpXBx7lN7e6upqbatK\nJBKq0Cz1VefPn8c777yjN5AvfvGLeO211zQJdPDgQdv8PiQPP/wwgFydHAt6Hjt2TNdATppe3EEO\n+ksCkCeRyU1dWigBb1uZuK3cJVReXq4SZfK96ejo0OSGKIzLGoBeT/Ja4m7zY/L8cn3X1tZqrFgS\ndYyEaGQt5LMcy8rKtFWN59mIxSc/CwaD+pqcqX711VcBQHv15edbqRXdkyLnYDCIzs5OtLe3Y2lp\nSd1JceEWFxcxOzurMwJ48LgUNlZUVOhFVFpaqhdGNBrVdjPR5ZM/irSnyYYqsvQ7duxQRQmJp6XT\naU9WlhMbXMgsj4l0vRR2yqYiYq3y3jlbvba2hsbGRmQyGWQyGc8YS2DT/WC3f2JiQi1HiamEQiGV\n25dEkliZclG//PLL+nxVVVXo6+vDhQsXkEgkEI1Gt1S/MIxPIgXf/MQKGh4e9twNlpeXVQZeXMWq\nqirs27cP6+vrGBwcVF2+kpISjI6OorGxUWt9pKxDNhsW6AwEAiqkIMOJUqkUnnjiCVWHFmEFIHcH\nlk1pampKrTbpOJERmfv378epU6dw7do1rK2toba2VmvtZOKcbEJSCiAJFhFPqKmpURl7sSLlcxH1\nm/n5eZ3jK5teTU2NbsLpdBoVFRWoq6tDTU0NksmkymxVVVWhu7sb09PTWo5TVVWFH//4x5rFPnDg\ngLW3fQRILEpGEAA5i4tDKUCuYV8sQ1HjBja1/6anp9Uik+eUudCCWJFcCiIxwzfeeEONAakHbGpq\nUouLlZw51ivXXVVVlc6+lTIy8ZAAb7+vWJBc6iIWLAssSHwd2LT8gsGg/jyZTGrChfuK3d5e+a7I\n5yiWr5QZydAxIGfViq6hlB4xBd/85ubm0NTUpD2n4k5KyYrUq8ViMUQiEdUZE+sqlUqhsbERhw4d\nwsDAgGY6q6urNQEi2TYp9pX+WbEgxUQXyy2VSqnAZ2VlJYLBIBKJBBobG7XLROZ8iIU3NjaG0dFR\nVYgBNmuMmpqaUFdXp+M0RR9wdXUVY2NjCIfD6pJKS5+oWrCVKDWA4l7LjaG8vFzrrjY2NrBz506d\nwTE/P4/bt29jfX0dDQ0NiMViOHPmjAas5Z9oxomlKtk044PDaiaSZeVsumwK0WhUC5vl5gdsNvT3\n9fVpFlceE8k3wH8YN7d17du3DwBUL29pacmTeJPkjIgdyKxpADqIC9jMAEuMHYBuKDdu3NCNSjQ3\n5XeBXGKHN0Q3Zi5trfKZscaknIfUCe7duxdArqj71q1b+jlKBQY3FkhReXNzs9ZT/v73v7/j8yr4\n5tfT06PzBtLpNC5cuICKigptDQuHw4hGo2htbVVV5oaGBpSWlmJqakprAb/xjW/gn//5nzE+Pq7W\njyQ4OKYhG5xko8RCEgtUEh+AtyI9EAggmUxqUXQmk9GND8gVpIqVxrEJqcuTOI64txsbG7h165ZH\nXUXkqXjjBTYFGSXJI18kYLPqXTbJYDCI3bt3Y3JyEufPn0cikdDNrKysDMPDwxgcHEQsFlN3e25u\nDq2trchkMti/f7+nfMAwioV7ouQsqsWLi4sYHBxEOBxGKBRCW1sbGhoaUFVVpRudVHRLOUtDQwNS\nqRRefPFFFTKQgmWxksrLy7VGSKwp+a+Y4iKZJXE4sYZEXDQej6O6ulqTMGK5AdBMqbwPHi4jrrcI\nkorFKlLzIoBQXl6OVCqFnTt3IplMaqyRN9iNjQ3Mzc2p1Sc6fSKgKnfw4eFhvPXWW1hdXUVnZydq\na2tx/fp1jI+PY3JyEjdv3lTZq0wmg97eXvT396OhoQHxeByNjY2+dYbG+0esqba2Nr1hvfLKK3pj\nFItp165dHiEJuXbEFd65c6eWwohlJh4R/z6w6SJyq2Rtba2WwrA1J3HjdDqtj7MrLNfdyMiIloiI\nFRYIBNSKlNeUGDMAbSMFoDfxYDDoKQtz4cSK9NcDm0mcjY0NjcW/9NJL+hnL+7h06ZIKPMj7HR4e\nVrGH9vZ2Tx2jS8E3v3g8jjNnzmB6elqLlNfW1vDoo49qCYzM0wiFQlhcXMTCwgLm5+dVbWJ1dRWX\nL1/WLK4IhsofUjbAdDqNuro6rWMTS0qUTSS7m0wmdWav6OaVlJR42uMkXicWmnSh8MS4aDSqU6zK\nysowMzODeDyOqakpTUTMzc2hpqZGVWqkeHVpaUm/HKyKwVqD0j4nsbva2lqcO3cO6+vr2LFjB/r6\n+rRT5fnnn8fExASqqqoQi8UwPDyMqqoqPP3005oxW11dVUtVYkvGB0c2r1OnTunmNj09jS9+8YsA\nNjOWKysrupEtLS2paylu5ZUrVzQ+KI/x5re2tqYuNmd4uSZOhFHFQ2ABVemqAjZneLCIRjAY1DCI\nuKpcuyjnMTMzo0PVZSoisOn9HDx4EFevXgXgLazmeKV8ZyVxxz8PBAJ4++23AUAzuIcPH8avfvUr\nADnvSzZ8cX+feOIJfe/s6ufjnoiZyhetoqICLS0t6O/v18HbIkMvvbQAcPPmTdTW1qrVIwomFRUV\nnuys1PjV1NToxri4uIhIJILa2lqNBS4tLWH79u1qsTU3N+voR552L+cqU9CkDQ6AttStra2pWy7n\nJQKVyWQSMzMzWo6TTCYRjUZRX1+PTCaDpaUlzVbLZLW5uTm1GiWrLc3a4vLKxhcMBvHee++hr68P\n/f39OH/+vH4eEiecmZnBrl278OCDD+LmzZsYGRlBR0eHSojJcHQeTWgYhmEYhmEYhmEYhmEYhmEY\nhmEYhmEYhmH8OXIJwLF7fRKG8SfArm3jT8ZLANYBlP6xXzSMPwOeBjAIYB5AAsAJAG339Iw+JPbF\n/NPwTeQKyE0e2fik8DpylmIYwHYAiwD+xz09I+NPyi0Aj93lMWEA7wI4ArP8jI8vt3D317ZQC+D/\nAvifH9nZ3APsi7k1G3/495cAZn3+zQDooGP+G4D/A2AChvHx5YNc248AmAOwAGAbgP9awPM1CsxN\nAMfv4vcPAjiH3E2lC2b5GR9f7vbaZtoAvADgf310p2N83LibC6QUwJvYzKB1Ibf55Z9OZBj3lg+z\n+QG5sM6f9aR7s0reH98EkPT5t4CcaxAC8BCA/wcgjtxGCAAjAD5d4PM1jPfL+7m281GOXNLD+IRy\nt3fHGP07iJzl14rchWIYHyfu9tr+SwCdf1hvB/A7AP/7oz6pQmKW30fLJP1LIBdQngBgo9GMP3f6\nAZwEkALwKoBTAP7LvTwh40/LEHIZLsP4pGHXtuFLDLmYhl/MwzD+XLFr2/DlEHKZrP9+r0/EMD5i\n7No2DMMoZgo+r/Dv/u7vtN/15s2b+vjx497EEw/UkTF6ADzzZWWKlCATrYDN8XoAPAOeeZTd9u3b\nPcfLSDwAOsYP2BwfCGxO6AI2J18JMp3LfZ3f/e53ur5+/brnGBnGDHjfm0xwA7yT1err6z3Hy6Qq\nIDcSUTh16pSuX375Zc8xsVgs7/N973vfs/mVH4J//Md/zNvLLQPK8yETy1z4Wnbha5CR6Wj5OHjw\n4F0dc+PGDd/n6u7uzvv4v//7v/seIyMoXWQgWD4OHDiQ9/Gthm394Ac/yPv4T3/60zuubcv2GoZR\nlBR8dGUymdT1yMiIrt2h2QMDA7oeGxvTtQyGBu68a7C1x1bZ0tKSrnl4snsHefbZZ3XNd0S+a/Kw\naT4vADpDFABu376d97ncO/r58+d1LYOu3ffCVqQ7/Plv/uZvdC2zSwHgP/7jP3TNVqz73IZRrNi3\nwDCMosQ2P8MwipKCu73sjrIL/MYbb3h+jwPB7PYlEglduy4gJwYYTiTw2nUHH3roIV3//ve/1zW7\n4By4ZTcVAFKplK7Z1Wb32n1NdoP53BhOULivWVa2+Sd8++23dc1JomAw6DkmnU7r2i8Qbdw9Q0ND\neR9/9913fY/xC/hzCOX9/mx+ft73mOnp6byPu9ejwNeyyy9+8Yu8j/N30+W1117L+zgn9ly6urry\nPv4v//Ivvsds9Rm4mOVnGEZRYpufYRhFiW1+hmEUJQWP+XFR7pNPPqnrV1991fN7XDDMxccc85qd\n9WopctEzxwn9CkavXr3qe278Op/97Gd1zaUug4ODnuO59GVjY7Pelct43BgHvw7H7/j4iYlNRfxI\nJOI5nstbODbJMUc3rsSlN1vFdgzjk4xZfoZhFCW2+RmGUZQU3O2NRqO63r17t6737dvn+b0TJ07o\nes+ePbrmsoErV654juGyDS7nYPy6QACve8z9mN///vd1/aUvfcn3eC4bYHeWS1i4zxjwurf8e1ye\nwr2cTzzxhO85c3kLlwH5lQC552l8OHp6evI+3tTU5HuMew0Jb731lu8x8Xg87+McNnHxK6Pyg69L\nF7+Snq2O8WOr8/K7Ni9cuOB7TGtr6/t+bbP8DMMoSmzzMwyjKCm428syVrdu3dI1Z3QB4MiRI7r+\nzGc+o+u//du/1fVvf/tbzzH/9E//pGt2LznDyma2K+fDXSUsPcXuBJ+/e7yfe8luq9tRwdlW1yUW\nWELIzTCzq81CEW5WmOHPY6sKe8P4JGOWn2EYRYltfoZhFCUFd3u5+ZmLkrkoF/BmtP7t3/5N13/1\nV3+la1ZBBoCvf/3ruuaM1EsvvaRrdgfdjDALLXAWjjOnly9f1vXDDz/sOf7SpUu65iwsu8eVlZWe\nY1hxeefOnXlfnxWnXeVfP63DrUIK7CrfbRbQ8MetPhC4MN6Fi/EZ1ml04UoI5uzZs77H+IVUrl27\nlvfxvr6+u36urVSZOSTD7N+/3/eYixcv+v7MD7/PMx9m+RmGUZTY5mcYRlFim59hGEVJwWN+XDbC\nDfs7duzw/B6XdHCMistZuAQG8MbTeJLZM888o2uOcbilMlyG0tvbq2sWCeUYmztFi98bx0W4q4Rj\ncYA3zsi/x2UzXA7DgqsA8Morr+iaRQ44ludO4tq2bZuutxLNNIxPMmb5GYZRlNjmZxhGUVJwt5dL\nNbjUxNXWYy1+LoPhY4aHhz3HsNvK7i27oDxPw20q5zKcT33qU7p+7rnn8r6+q4XHszbc9+N3zt/+\n9rfz/oybuvk83bIVdlt57TcGE9i6JMH44PgN095qAPi5c+fyPv7888/7HnP8+PG8j7uhI8ZPDMEP\nNzzD+JWTbPU+OdTCbDWAfCtBCD/8Brrnwyw/wzCKEtv8DMMoSgru9jIdHR26XlhY8PyMXTWWZ+cs\nJndbAN4mfe7KYJ07/h3X/XvggQfyHs+mNLuTnK0GgKNHj+qaJfbZhXA1yrjynUMCnOFmbT/O6Lrn\nyZ8hnzN3jgDezhrT8zOKFbP8DMMoSmzzMwyjKCm428tFvezmuRmk9vZ2XbN7yW4iPxfgdeFGR0fz\nvj5nVN1sLRdWs9vN8tzsKrObC3hd1ffee0/XW+nx8ftk6Xx2mzmL64ox8GQ4v4Jl932yG+zXpG7c\nPa6+o8B/fxc/SfjTp0/7HlNfX5/38du3b/se4ydU4Pf6XO3g4qcB+c477/gew/qcjFu9wPhJ/G+V\nIebv0B/DLD/DMIoS2/wMwyhKCu72smvILpfrfrFpzW4aZ05Zvw7wmv08Gc4v8+sOM2dXmV1F/j0e\nbO5KxfP/P/bYY7p2M7QMu9T333+/rtlt5nNxs+L8OfG5cUiBC8YBr74c/z0Mo5gwy88wjKLENj/D\nMIoS2/wMwyhKCh7z49gel6q46Wvu5OD4Fce13GZpjpNNT0/nPYbhWCDgjflxVwV3RHBczi054PIY\n7hb50Y9+lPf1AaCrq0vXHP9jkQRO+buxUdb942n1/FzcIQN4P1tX9MD44HB5EsPXogvrTjIzMzO+\nx/j9bKt5LK52peCWQQnufBqms7Mz7+PPPvus7zGPPvpo3se3mm/ilrL9secC/Evc8mFXvmEYRYlt\nfoZhFCUFd3vZ1WSdPrfshE1ePobdSXfsXn9/v67ZBWG3kZ+XhRUAb/cIuwPsdrNmoOuCNjQ06Jpd\nE3ZH2J0GvNL7/PpcnsLv3+0iYLeVq+X5GHahAe/nYaUuRrFilp9hGEWJbX6GYRQlBXd72eXiTCVn\nVAFvFsgvI+l2WPDz+QkGsGvJE9oAr9vI3SJ+rrLr9vL0Nn4dFkBwOzT4fXMYgOHPjF8D8HZ4sAvL\nn4WbleYuGVcowfjg+HXyuH8zxu2+EdyQDMPXNrOVVL37/RL4On0/rwHcWSUhbCWj7173gl+GHPAf\nt3Dffff5HrNVN5WLWX6GYRQltvkZhlGUFNztjUajun7kkUd0ffLkSc/vcbZ0z549uubMqesmssnL\nGU6eAvUXf/EXumaRA8AroMCT3B5//HFdc4HnW2+95Tme3XA+T9bc279/v+cYPgd2Tdi14LVblMqf\nJxc2+/0O4NVHdD8DwygWzPIzDKMosc3PMIyixDY/wzCKkoLH/Dj+xqUl7pwD7qro6enRNZcGuPr/\nXPbBJRyTk5N5n4uFAABvSQy/PneO8EhIN03PcUKOs3HZgPs+ObbJ58nvhdfuXAMub+HfY6EIt6uE\n56X4zf0w7p7t27fnfZyvHxe/UiO+Flz8yka+/vWvb3F2+eF4NLOVQIDf3I1nnnnG9xgWHWH8yrsA\n73eNcTuWGL/5Jvkwy88wjKLENj/DMIqSe6rn9/rrr+va7eJg05rdRq7uPnz4sOcYLnW5dOmSrrm0\ng10G9zX9fo8fZ2EBVxSAK+x5vgh3iLiaa+x2cFcGH3PhwgVdszvuvg5XxLNgAj8v4HV73Z8ZRrFg\nlp9hGEWJbX6GYRQlBXd72c17/vnnN0/Eaf5m3TzOfPHjbrM2d1iwe8yN/JwtdV1IznCxe8tag9xt\nwZlrwJuJ5nPx0yYEvG4wZ7f4uVgnkF1WABgbG9M1hwo42+sKQHBWkp/vueeeg/HB4Ww785Of/MT3\nGD9J9iNHjvge46fBePPmTd9j/MIbfl1BfvL2wJ3am+8HP+n9rTqM/AQU9u7d63vMvn373vc5meVn\nGEZRYpufYRhFScHdXs7cspvmFnsODQ3pmouH2YVzp7fxc/PzcWHz+fPndf3Zz37Wczyb85wJZheS\n3WG3eJhdVX59dund98nuBb8+u/ccKnCLT9nt5fd//fp1XbvCBuwCsWiEYRQTZvkZhlGU2OZnGEZR\nUnC3l11V7nl0s07sHnK2lNduBomzt1zky72AXGTNUvWA19XlrHAmk9E1Z9rcrBtnnzlzy+/NlS1n\nl5qzx+wCc0bYzdxyAbZfhvjXv/615xjWJ/STCjfunmPHjuV9/MaNG77HvPnmm3kfdwfNM1/+8pfz\nPr7VoHM3RCP4ZYH9fn+r19mqH9mv59YNXTHnzp3L+ziHdFz8MsT5MMvPMIyixDY/wzCKEtv8DMMo\nSgoe8+OyD443uR0e/DMeiTc9Pa1rP70vwOv7c2zuscce07U7g+PTn/60rs+cOaNrjrnxc7kiBXw+\nXBLDMT+3K+XQoUO65vkgXJLD5Syunh/PHeE4DccSuVQI8L63+++/H4ZRjJjlZxhGUWKbn2EYRUnB\n3V4uJzlw4ICu3ZS/X+cDu8euHh9Pn+fyFIbdQXYzAa8AAndYsNvKpQGu28suMbvdX/va13Ttpvb9\nSnf4ubnsh91pwPt+eM3n3NXV5fuafs34xt3DIQjmwQcf9D2GwziMWxLF+AkY+MnoA16tyw+Ln4z+\nN7/5Td9jXBER4Ze//KXvMX6f51YalO4I3K0wy88wjKLENj/DMIqSgru93KHAmU/X/GdJ+N27d+ua\n3UG3O6G3t1fX7LZOTU3pmrOl7hQonjDFz81dISzG4JrfnFVlt5sfd7O1V65cyfszPmd2+933zJ8H\nu7BuhpfhDDNn0g2jmDDLzzCMosQ2P8MwipKCu73vvvuurrfKnHJWl6XW2e1zM1gsic2N/TxcnLOw\nnB0FvEPM+bn49f2k6gFvJpcLky9fvqxr181k95gHOHNWl8/TlRDnoeM8yW0rSfP9+/fr+m6GPBtb\n4ycSsVUIwi8L62owMh0dHXkf30pYwC2uF9zqAYG1IV38sr1cbeHidz36ZbsB7/eRGR4e9j3mq1/9\nat7HX3jhhTseM8vPMIyixDY/wzCKkoK7vZzFfeWVV3TtugzcJ3vx4kVdc0aXNfsAb1b2tdde0zVL\nv/PkJzdbyy7kk08+qWt2NTk7y1L7gHdiHGduuXjZNfP7+vp0zTpl7B6za8xZbMCbCT99+rSu2e13\ntRJZ1v/tt9+GYRQjZvkZhlGU2OZnGEZRYpufYRhFScFjflw2wvE3d84BN0JzGQyXrXD8D/CWoTQ3\nN+t6165duuaygy984Que41lAgH+PtfW2Elbg8haex+EnOAB4S2q444Q/p+7ubl1zXBLwxiC5bIJf\n320Q5+feqgzDuDs4zsxsVZrhzpERHn30Ud9j/GaCbDV3g+e2MB+kbIXjzMxWYgx+IgWsr+ni935O\nnDjhe8ynPvUp35+5mOVnGEZRYpufYRhFScHdXjan2R113UEe3cdV6Fz17YoEcFX8vn37dM2u3dGj\nR3XNmoGAt9SEK+K5C4JLSNi1BLxiBOyq8/m7nSz8OuzS8nvj8qDBwUHP8VwSxOfJYQMOAbjPzaMv\nDaOYMMvPMIyixDY/wzCKkoK7vdwtwfp57hR4duFYBp4zmq4LyW4ju6ScoeVMGWvzucewS+4nPuBO\nnOPuC24yZ3l711Xn7DVTUlKia84IuxkwztxyxwpL17vN66z759fwbtw9PAaB2Up2/XOf+1zex/2a\n+gHv+AeGqxVc/MY6+Enfc4WBi1+FAHdSubjfNYFDRe/3+b70pS/5HsPdS38Ms/wMwyhKbPMzDKMo\nKbjbe/XqVV3v2bNH166u2VNPPaVrduE4I+u6gOxCsn4XFxlzYXJbW5vneH4+dgc5i8xFqewCA96M\ntV8xtCvGwK/pFk3ne303K86F0eze8vm7Ygi/+c1vdP3666/nfU3D+KRjlp9hGEWJbX6GYRQltvkZ\nhlGUFDzmxx0W/f39uj5+/Ljn91j0kwUDuFSGOx8Ab8yMOzE4zsZlBzxPBACOHTuma46fcWqfy2vc\nmCHHI7nshs/LjRMyHJvk0gQu+3FLZXgmCTeP8++5Teo/+9nPdO12uRgfHL/SDD9RAcBfJGCreRxc\nIsa4pVcMdzwxfqUhW5Wg+OGWnjFcusW4Qh0Ml3Exhw8f9j3mH/7hH3x/5mKWn2EYRYlCz1P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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f1 = fW.copy()\n", "for j in arange(Jmin,Jmax+1): \n", " A = f1[:2**(j+1):,:2**(j+1):]\n", " for d in arange(1,3):\n", " if d==1:\n", " Coarse = A[:2**j:,:]\n", " Detail = A[2**j:2**(j+1):,:]\n", " else:\n", " Coarse = A[:,:2**j:]\n", " Detail = A[:,2**j:2**(j+1):]\n", " Coarse = cconv(upsampling(Coarse,d),reverse(h),d)\n", " Detail = cconv(upsampling(Detail,d),reverse(g),d)\n", " A = Coarse + Detail\n", " j1 = Jmax-j\n", " if j1>0 and j1<5:\n", " imageplot(A, 'j=' + str(int(j)), [2,2,j1])\n", " f1[:2**(j+1):,:2**(j+1):] = A" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Check that we recover exactly the original image." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error |f-f1|/|f| = 8.52769256341e-12\n" ] } ], "source": [ "print( 'Error |f-f1|/|f| = ' + str(norm(f-f1)/norm(f)) )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Linear 2-D Wavelet Approximation" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Linear approximation is performed by setting to zero the fine scale wawelets coefficients\n", "and then performing the inverse wavelet transform.\n", "\n", "Here we keep only 1/16 of the wavelet coefficient, thus calculating an $m$\n", "term approximation with $m=n^2/16$." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "fW = perform_wavortho_transf(f,Jmin,+1,h)\n", "eta = 4\n", "fWLin = zeros((n,n))\n", "fWLin[:n/eta:,:n/eta:] = fW[:n/eta:,:n/eta:]\n", "fLin = perform_wavortho_transf(fWLin,Jmin,-1,h)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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O2Wym09NTnZ6eBvvVg4Bra2vBtAD+w669fPmyrl+/rlu3bunevXu6ffu2Dg4O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\nEBQ4sWCLUgQozMnlcgEB8qg3gTXKQNFWoBvY7LPZLHTZw4Z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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "elin = snr(f,fLin)\n", "imageplot(clamp(fLin), 'Linear, SNR=' + str(elin), [1,2,2] )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Non-Linear 2-D Wavelet Approximation" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "A non-linear $m$-term approximation is obtained by keeping only the $m$\n", "largest coefficients, which creates the smallest possible error.\n", "\n", "\n", "Removing the smallest coefficient, to keep the $m$-largest, is\n", "equivalently obtainedby thresholding the coefficients to\n", "set to 0 the smallest coefficients. \n", "\n", "\n", "First select a threshold value (the largest the threshold, the more\n", "agressive the approximation)." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "T = .2" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Then set to 0 coefficients with magnitude below the threshold." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "fWT = fW * (abs(fW)>T)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display thresholded coefficients." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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fb9x8882XPHbkyJGmAvflnrNZsKmCvlgQC1cMG1+MUqnUNDc2EAio/0uhUGBh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\nFEVRRvgvL1TouG0K3JcAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "subplot(1,2,1)\n", "plot_wavelet(fW,Jmin);\n", "subplot(1,2,2)\n", "plot_wavelet(fWT,Jmin);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Plot the (log of) the coefficient in decaying order." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m = round((n**2)/(eta**2))\n", "v = reverse( msort(abs(fW).ravel()) )\n", "plot(log10(v))\n", "axis('tight');" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Find the thresholds $T$ so that the number $m$ of remaining coefficients in the threshold coefficients\n", "are $m=n^2/16$. " ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "T = v[m]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the corresponding non-linear approximation." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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F1yGjUUpaNUwkEsHS0hK63S6CwaCofgCo1+uyYDS9OE6/34/V1VUcOXJENJN1nMlkEl6v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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fWT = fW * (abs(fW)>=T)\n", "fnl = perform_wavortho_transf(fWT,Jmin,-1,h)\n", "enl = snr(f,fnl)\n", "imageplot(clamp(fnl), 'Non-linear, SNR=' + str(enl), [1,2,2] )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Exercise" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "*Exercise 1:* Compare the approximation obtained using wavelet with different number of vanishing moments." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "*Exercise 2:* Implement a 2-D separable wavelet transform." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "*Exercise 3:* Display a 2-D wavelet by applying the backward transform to a Dirac (i.e. all zeros excepted a single 1 at a well-chosen position)." ] }, { "cell_type": "raw", "metadata": { "deletable": true, "editable": true }, "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": "3.4.5" } }, "nbformat": 4, "nbformat_minor": 0 }