{"nbformat_minor": 0, "worksheets": [{"cells": [{"source": ["Volumetric wavelet Data Processing\n", "==================================\n", "\n*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_matlab/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n", "$\\newcommand{\\choice}[1]{ \\left\\{  \\begin{array}{l} #1 \\end{array} \\right. }$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$\n"], "metadata": {}, "cell_type": "markdown"}, {"source": ["This numerical tour explores volumetric (3D) data processing."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 2, "cell_type": "code", "language": "python", "metadata": {}, "input": ["addpath('toolbox_signal')\n", "addpath('toolbox_general')\n", "addpath('solutions/multidim_2_volumetric')"]}, {"source": ["For Scilab user (otherwise there is not enough memory).\n", "WARNING: you should extend the stack size only ONCE."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 3, "cell_type": "code", "language": "python", "metadata": {}, "input": ["extend_stack_size(10);"]}, {"source": ["3D Volumetric Datasets\n", "----------------------\n", "\n", "\n", "We load a volumetric data."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 4, "cell_type": "code", "language": "python", "metadata": {}, "input": ["name = 'vessels';\n", "options.nbdims = 3;\n", "M = read_bin(name, options);\n", "M = rescale(M);"]}, {"source": ["size of the image (here it is a cube)."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 5, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = size(M,1);"]}, {"source": ["We can display some horizontal slices."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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nCC1N3p3uq2azGYaxxJiz2Ywrh81naiPTTIrVanXv3j18+WKxqNfrDI765JNP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\nK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6PQiwH6VTVuZGSE28tms9TtxDQ7i+mgVM9KxUIMaQUamML65JfVarXb7U5M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\nqPdLMLcFiYHU1bu1vuEK8tHyMXJyRHlyt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MMpKoBAC7aQoSaBM6ZNhcvn0elUSsM0Mj5F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\nyshAMp9GJxS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J/SAiCCWjKnvYbDb39vbW19c3NzeZo0un02iNfPToES10PB6PxWLtdhu3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\nh1MJZ8AcHBwcHE4l/h8bp3eerW1p0QAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "cell_type": "code", "language": "python", "metadata": {}, "input": ["slices = round(linspace(10,n-10,4));\n", "clf;\n", "for i=1:length(slices)\n", "    s = slices(i);\n", "    imageplot( M(:,:,s), strcat(['Z=' num2str(s)]), 2,2,i );\n", "end"]}, {"source": ["We can display an isosurface of the dataset (here we sub-sample to speed\n", "up the computation)."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["sel = 1:2:n;\n", "clf;\n", "isosurface( M(sel,sel,sel), .5);\n", "axis('off');"]}, {"source": ["3D Haar Transform\n", "-----------------\n", "An isotropic 3D Haar transform recursively extract details wavelet\n", "coefficients by performing local averages/differences along the X/Y/Z axis.\n", "\n", "\n", "We apply a step of Haar transform in the X/Y/Z direction\n", "\n", "initialize the transform"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["MW = M;"]}, {"source": ["average/difference along X"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["MW = cat3(1, (MW(1:2:n,:,:)+MW(2:2:n,:,:))/sqrt(2), (MW(1:2:n,:,:)-MW(2:2:n,:,:))/sqrt(2) );"]}, {"source": ["average/difference along Y"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["MW = cat3(2, (MW(:,1:2:n,:)+MW(:,2:2:n,:))/sqrt(2), (MW(:,1:2:n,:)-MW(:,2:2:n,:))/sqrt(2) );"]}, {"source": ["average/difference along Z"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["MW = cat3(3, (MW(:,:,1:2:n)+MW(:,:,2:2:n))/sqrt(2), (MW(:,:,1:2:n)-MW(:,:,2:2:n))/sqrt(2) );"]}, {"source": ["Display a horizontal and vertical slice to see the structure of the coefficients."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(MW(:,:,30), 'Horizontal slice', 1,2,1);\n", "imageplot(squeeze(MW(:,30,:)), 'Vertical slice', 1,2,2);"]}, {"source": ["__Exercise 1__\n", "\n", "Implement the forward wavelet transform by iteratively applying these\n", "transform steps to the low pass residual.\n", "nitialize the transform"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo1()"]}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Volumetric Data Haar Approximation\n", "----------------------------------\n", "An approximation is obtained by keeping only the largest coefficients.\n", "\n", "\n", "We threshold the coefficients to perform |m|-term approximation.\n", "\n", "number of kept coefficients"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["m = round(.01*n^3);\n", "MWT = perform_thresholding(MW, m, 'largest');"]}, {"source": ["__Exercise 2__\n", "\n", "Implement the backward transform to compute an approximation |M1| from\n", "the coefficients |MWT|."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo2()"]}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display the approximation as slices."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["s = 30;\n", "clf;\n", "imageplot( M(:,:,s), 'Original', 1,2,1 );\n", "imageplot( clamp(M1(:,:,s)), 'Approximation', 1,2,2 );"]}, {"source": ["Display the approximated isosurface."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["sel = 1:2:n;\n", "clf;\n", "isosurface( M1(sel,sel,sel), .5);\n", "axis('off');"]}, {"source": ["Linear Volumetric Denoising \n", "----------------------------\n", "Linear denoising is obtained by low pass filtering.\n", "\n", "\n", "We add a Gaussian noise to the image.\n", "\n", "noise level."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["sigma = .06;\n", "Mnoisy = M + sigma*randn(n,n,n);"]}, {"source": ["Display slices of the noisy data."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(Mnoisy(:,:,n/2),'X slice', 1,2,1);\n", "imageplot(squeeze(Mnoisy(:,n/2,:)),'Y slice', 1,2,2);"]}, {"source": ["A simple denoising method performs a linear filtering of the data.\n", "\n", "\n", "We build a Gaussian filter of width |sigma|.\n", "\n", "construct a 3D grid"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["x = -n/2:n/2-1;\n", "[X,Y,Z] = ndgrid(x,x,x);"]}, {"source": ["gaussian filter"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["s = 2; % width\n", "h = exp( -(X.^2 + Y.^2 + Z.^2)/(2*s^2) );\n", "h = h/sum(h(:));"]}, {"source": ["The filtering is computed over the Fourier domain."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["Mh = real( ifftn( fftn(Mnoisy) .* fftn(fftshift(h)) ) );"]}, {"source": ["Display denoised slices."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["i = 40;\n", "clf;\n", "imageplot( Mnoisy(:,:,i), 'Noisy', 1,2,1 );\n", "imageplot( Mh(:,:,i), 'Denoised', 1,2,2 );"]}, {"source": ["Display denoised iso-surface."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["sel = 1:2:n;\n", "clf;\n", "isosurface( Mh(sel,sel,sel), .5);\n", "axis('off');"]}, {"source": ["__Exercise 3__\n", "\n", "Select the optimal blurring width |s| to reach the smallest possible\n", "SNR. Keep the optimal denoising |Mblur|"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo3()"]}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display optimally denoised iso-surface."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["sel = 1:2:n;\n", "clf;\n", "isosurface( Mblur(sel,sel,sel), .5);\n", "axis('off');\n", "title(['Filtering, SNR=' num2str(snr(M,Mblur),3) 'dB']);"]}, {"source": ["Non-Linear Wavelet Volumetric Denoising \n", "----------------------------------------\n", "Denoising is obtained by removing small amplitude coefficients that\n", "corresponds to noise."], "metadata": {}, "cell_type": "markdown"}, {"source": ["__Exercise 4__\n", "\n", "Perforn Wavelet denoising by thresholding the wavelet coefficients of\n", "Mnoisy. Test both hard thresholding and soft thresholding to determine\n", "the optimal threshold and the corresponding SNR.\n", "Record the optimal result |Mwav|."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo4()"]}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display denoised iso-surface with optimal soft thresholding."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["sel = 1:2:n;\n", "clf;\n", "isosurface( Mwav(sel,sel,sel), .5);\n", "title(['Soft thresholding, SNR=' num2str(snr(M,Mwav),3) 'dB']);\n", "axis('off');"]}, {"source": ["Orthogonal wavelet thresholdings suffers from blocking artifacts.\n", "This can be aleviated by performing a cycle spinning denoising, which\n", "average the denosing result of translated version of the signal.\n", "\n", "\n", "A typical cycle spinning process is like this.\n", "\n", "maximum translation"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["w = 4;"]}, {"source": ["list of translations"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["[dX,dY,dZ] = ndgrid(0:w-1,0:w-1,0:w-1);"]}, {"source": ["initialize spinning process"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["Mspin = zeros(n,n,n);"]}, {"source": ["spin"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["for i=1:w^3\n", "    % shift the image\n", "    MnoisyC = circshift(Mnoisy, [dX(i) dY(i) dZ(i)]);\n", "    % denoise the image to get a result M1\n", "    M1 = MnoisyC; % replace this line by some denoising\n", "    % shift inverse\n", "    M1 = circshift(M1, -[dX(i) dY(i) dZ(i)]);\n", "    % average the result\n", "    Mspin = Mspin*(i-1)/i + M1/i;\n", "end"]}, {"source": ["__Exercise 5__\n", "\n", "Implement cycle spinning hard thresholding with |T=3*sigma|."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo5()"]}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display denoised iso-surface."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["sel = 1:2:n;\n", "clf;\n", "isosurface( Mspin(sel,sel,sel), .5);\n", "title(['Cycle spinning, SNR=' num2str(snr(M,Mspin),3) 'dB']);\n", "axis('off');"]}, {"source": ["Higher Order Daubechies Wavelets\n", "--------------------------------\n", "Similarely to the Haar transform, wavelets with more vanishing moments\n", "are obtained with filtering and subsampling (pyramidal algorihtm).\n", "\n", "\n", "First we create the filters for 4 vanishing moments."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["[h,g] = compute_wavelet_filter('Daubechies',2*4);"]}, {"source": ["Then we initialize the wavelet transform with the 3D image itself, and set the current scale."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["MW = M;\n", "j = log2(n)-1;"]}, {"source": ["We transform by filtering + sub-sampling the low pass residual along the three directions."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["A = MW(1:2^(j+1),1:2^(j+1),1:2^(j+1));\n", "for d=1:3\n", "    a = cat(d, subsampling(cconv(A,h,d),d), subsampling(cconv(A,g,d),d) );\n", "end\n", "MW(1:2^(j+1),1:2^(j+1),1:2^(j+1)) = A;"]}, {"source": ["__Exercise 6__\n", "\n", "Implement the full 3D forward wavelet transform by applying these steps\n", "for decaying scales |j| toward 0."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo6()"]}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Threshold the coefficients."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["MWT = perform_thresholding(MW,m,'largest');"]}, {"source": ["Display the coefficients and thresholded coefficients for one slice."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "subplot(1,2,1);\n", "plot_wavelet(MW(:,:,n/8));\n", "subplot(1,2,2);\n", "plot_wavelet(MWT(:,:,n/8));"]}, {"source": ["Initialize the backward transform."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["M1 = MWT;\n", "j = 0;"]}, {"source": ["Undo one step of the wavelet transform.\n", "_Note:_ |subselectdim(A,sel,1)| is equivalent to |A(sel,:,:)|\n", "while |subselectdim(A,sel,2)| is equivalent to |A(:,sel,:)|."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["A = M1(1:2^(j+1),1:2^(j+1),1:2^(j+1));\n", "for d=1:3\n", "    W = subselectdim(A,2^j+1:2^(j+1),d);\n", "    A = subselectdim(A,1:2^j,d);\n", "    A = cconv(upsampling(A,d),reverse(h),d) + cconv(upsampling(W,d),reverse(g),d);\n", "end\n", "M1(1:2^(j+1),1:2^(j+1),1:2^(j+1)) = A;"]}, {"source": ["__Exercise 7__\n", "\n", "Implement the full 3D backward wavelet transform by applying these steps\n", "for increasing scales |j|."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo7()"]}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display approximated iso-surface."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["sel = 1:2:n;\n", "clf;\n", "isosurface( M1(sel,sel,sel), .5);\n", "title(['Soft thresholding, SNR=' num2str(snr(M,M1),3) 'dB']);\n", "axis('off');"]}, {"source": ["Denoising Daubechies Wavelets\n", "-----------------------------\n", "Better denoising results are obtined by thresholding orthogonal wavelet\n", "coefficients."], "metadata": {}, "cell_type": "markdown"}, {"source": ["__Exercise 8__\n", "\n", "Implement denoising by soft and hard thresholding Daubechies wavelet\n", "coefficients."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo8()"]}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display denoised iso-surface with optimal soft thresholding."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["sel = 1:2:n;\n", "clf;\n", "isosurface( Mwav(sel,sel,sel), .5);\n", "title(['Soft thresholding, SNR=' num2str(snr(M,Mwav),3) 'dB']);\n", "axis('off');"]}, {"source": ["__Exercise 9__\n", "\n", "Implement cycle spinning hard thresholding with Daubechies wavelets with |T=3*sigma|."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo9()"]}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display denoised iso-surface."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "cell_type": "code", "language": "python", "metadata": {}, "input": ["sel = 1:2:n;\n", "clf;\n", "isosurface( Mspin(sel,sel,sel), .5);\n", "title(['Cycle spinning, SNR=' num2str(snr(M,Mspin),3) 'dB']);\n", "axis('off');"]}], "metadata": {}}], "nbformat": 3, "metadata": {"kernelspec": {"name": "matlab_kernel", "language": "matlab", "display_name": "Matlab"}, "language_info": {"mimetype": "text/x-matlab", "name": "matlab", "file_extension": ".m", "help_links": [{"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md", "text": "MetaKernel Magics"}]}}}