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1 %% Dictionary Learning for Image Denoising - KSVD vs Recursive Least Squares
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2 %
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3 % This file contains an example of how SMALLbox can be used to test different
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4 % dictionary learning techniques in Image Denoising problem.
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5 % It calls generateImageDenoiseProblem that will let you to choose image,
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6 % add noise and use noisy image to generate training set for dictionary
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7 % learning.
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8 % Two dictionary learning techniques were compared:
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9 % - KSVD - M. Elad, R. Rubinstein, and M. Zibulevsky, "Efficient
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10 % Implementation of the K-SVD Algorithm using Batch Orthogonal
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11 % Matching Pursuit", Technical Report - CS, Technion, April 2008.
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12
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13
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14
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15 % Centre for Digital Music, Queen Mary, University of London.
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16 % This file copyright 2011 Ivan Damnjanovic.
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17 %
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18 % This program is free software; you can redistribute it and/or
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19 % modify it under the terms of the GNU General Public License as
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20 % published by the Free Software Foundation; either version 2 of the
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21 % License, or (at your option) any later version. See the file
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22 % COPYING included with this distribution for more information.
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23 %
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24 %%
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25
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26
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27
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28 % If you want to load the image outside of generateImageDenoiseProblem
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29 % function uncomment following lines. This can be useful if you want to
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30 % denoise more then one image for example.
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31 % Here we are loading test_image.mat that contains structure with 5 images : lena,
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32 % barbara,boat, house and peppers.
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33 clear;
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34 TMPpath=pwd;
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35 FS=filesep;
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36 [pathstr1, name, ext] = fileparts(which('SMALLboxSetup.m'));
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37 cd([pathstr1,FS,'data',FS,'images']);
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38 load('test_image.mat');
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39 cd(TMPpath);
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40
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41 % Deffining the noise levels that we want to test
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42
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43 noise_level=[10 20 25 50 100];
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44
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45 % Here we loop through different noise levels and images
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46
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47 for noise_ind=4:4
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48 for im_num=1:1
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49
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50 % Defining Image Denoising Problem as Dictionary Learning
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51 % Problem. As an input we set the number of training patches.
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52
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53 SMALL.Problem = generateImageDenoiseProblem(test_image(im_num).i, 40000, '',256, noise_level(noise_ind));
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54 SMALL.Problem.name=int2str(im_num);
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55
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56 Edata=sqrt(prod(SMALL.Problem.blocksize)) * SMALL.Problem.sigma * SMALL.Problem.gain;
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57 maxatoms = floor(prod(SMALL.Problem.blocksize)/2);
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58
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59 % results structure is to store all results
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60
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61 results(noise_ind,im_num).noisy_psnr=SMALL.Problem.noisy_psnr;
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62
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63 %%
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64 % Use KSVD Dictionary Learning Algorithm to Learn overcomplete dictionary
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65
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66 % Initialising Dictionary structure
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67 % Setting Dictionary structure fields (toolbox, name, param, D and time)
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68 % to zero values
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69
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70 SMALL.DL(1)=SMALL_init_DL();
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71
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72 % Defining the parameters needed for dictionary learning
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73
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74 SMALL.DL(1).toolbox = 'KSVD';
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75 SMALL.DL(1).name = 'ksvd';
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76
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77 % Defining the parameters for KSVD
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78 % In this example we are learning 256 atoms in 20 iterations, so that
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79 % every patch in the training set can be represented with target error in
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80 % L2-norm (Edata)
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81 % Type help ksvd in MATLAB prompt for more options.
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82
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83
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84 SMALL.DL(1).param=struct(...
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85 'Edata', Edata,...
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86 'initdict', SMALL.Problem.initdict,...
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87 'dictsize', SMALL.Problem.p,...
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88 'exact', 1, ...
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89 'iternum', 20,...
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90 'memusage', 'high');
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91
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92 % Learn the dictionary
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93
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94 SMALL.DL(1) = SMALL_learn(SMALL.Problem, SMALL.DL(1));
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95
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96 % Set SMALL.Problem.A dictionary
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97 % (backward compatiblity with SPARCO: solver structure communicate
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98 % only with Problem structure, ie no direct communication between DL and
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99 % solver structures)
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100
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101 SMALL.Problem.A = SMALL.DL(1).D;
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102 SMALL.Problem.reconstruct = @(x) ImageDenoise_reconstruct(x, SMALL.Problem);
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103
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104 %%
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105 % Initialising solver structure
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106 % Setting solver structure fields (toolbox, name, param, solution,
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107 % reconstructed and time) to zero values
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108
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109 SMALL.solver(1)=SMALL_init_solver;
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110
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111 % Defining the parameters needed for image denoising
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112
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113 SMALL.solver(1).toolbox='ompbox';
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114 SMALL.solver(1).name='omp2';
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115 SMALL.solver(1).param=struct(...
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116 'epsilon',Edata,...
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117 'maxatoms', maxatoms);
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118
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119 % Denoising the image - find the sparse solution in the learned
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120 % dictionary for all patches in the image and the end it uses
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121 % reconstruction function to reconstruct the patches and put them into a
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122 % denoised image
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123
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124 SMALL.solver(1)=SMALL_solve(SMALL.Problem, SMALL.solver(1));
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125
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126 % Show PSNR after reconstruction
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127
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128 SMALL.solver(1).reconstructed.psnr
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129
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130 %%
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131 % For comparison purposes we will denoise image with overcomplete DCT
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132 % here
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133 % Set SMALL.Problem.A dictionary to be oDCT (i.e. Problem.initdict -
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134 % since initial dictionaruy is already set to be oDCT when generating the
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135 % denoising problem
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136
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137
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138 % Initialising solver structure
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139 % Setting solver structure fields (toolbox, name, param, solution,
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140 % reconstructed and time) to zero values
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141
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142 SMALL.solver(2)=SMALL_init_solver;
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143
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144 % Defining the parameters needed for image denoising
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145
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146 SMALL.solver(2).toolbox='ompbox';
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147 SMALL.solver(2).name='omp2';
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148 SMALL.solver(2).param=struct(...
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149 'epsilon',Edata,...
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150 'maxatoms', maxatoms);
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151
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152 % Initialising Dictionary structure
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153 % Setting Dictionary structure fields (toolbox, name, param, D and time)
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154 % to zero values
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155
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156 SMALL.DL(2)=SMALL_init_DL('TwoStepDL', 'MOD', '', 1);
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157
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158
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159 % Defining the parameters for MOD
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160 % In this example we are learning 256 atoms in 20 iterations, so that
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161 % every patch in the training set can be represented with target error in
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162 % L2-norm (EData)
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163 % Type help ksvd in MATLAB prompt for more options.
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164
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165
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166 SMALL.DL(2).param=struct(...
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167 'solver', SMALL.solver(2),...
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168 'initdict', SMALL.Problem.initdict,...
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169 'dictsize', SMALL.Problem.p,...
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170 'iternum', 40,...
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171 'show_dict', 1);
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172
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173 % Learn the dictionary
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174
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175 SMALL.DL(2) = SMALL_learn(SMALL.Problem, SMALL.DL(2));
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176
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177 % Set SMALL.Problem.A dictionary
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178 % (backward compatiblity with SPARCO: solver structure communicate
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179 % only with Problem structure, ie no direct communication between DL and
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180 % solver structures)
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181
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182 SMALL.Problem.A = SMALL.DL(2).D;
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183 SMALL.Problem.reconstruct = @(x) ImageDenoise_reconstruct(x, SMALL.Problem);
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184
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185 % Denoising the image - find the sparse solution in the learned
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186 % dictionary for all patches in the image and the end it uses
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187 % reconstruction function to reconstruct the patches and put them into a
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188 % denoised image
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189
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190 SMALL.solver(2)=SMALL_solve(SMALL.Problem, SMALL.solver(2));
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191
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192 %%
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193 % In the b1 field all patches from the image are stored. For RLS-DLA we
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194 % will first exclude all the patches that have l2 norm smaller then
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195 % threshold and then take min(40000, number_of_remaining_patches) in
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196 % ascending order as our training set (SMALL.Problem.b)
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197
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198 X=SMALL.Problem.b1;
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199 X_norm=sqrt(sum(X.^2, 1));
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200 [X_norm_sort, p]=sort(X_norm);
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201 p1=p(X_norm_sort>Edata);
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202 if size(p1,2)>40000
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203 p2 = randperm(size(p1,2));
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204 p2=sort(p2(1:40000));
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205 size(p2,2)
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206 SMALL.Problem.b=X(:,p1(p2));
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207 else
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208 size(p1,2)
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209 SMALL.Problem.b=X(:,p1);
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210
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211 end
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212
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213 % Forgetting factor for RLS-DLA algorithm, in this case we are using
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214 % fixed value
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215
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216 lambda=0.9998
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217
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218 % Use Recursive Least Squares
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219 % to Learn overcomplete dictionary
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220
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221 % Initialising Dictionary structure
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222 % Setting Dictionary structure fields (toolbox, name, param, D and time)
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223 % to zero values
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224
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225 SMALL.DL(3)=SMALL_init_DL();
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226
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227 % Defining fields needed for dictionary learning
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228
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229 SMALL.DL(3).toolbox = 'SMALL';
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230 SMALL.DL(3).name = 'SMALL_rlsdla';
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231 SMALL.DL(3).param=struct(...
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232 'Edata', Edata,...
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233 'initdict', SMALL.Problem.initdict,...
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234 'dictsize', SMALL.Problem.p,...
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235 'forgettingMode', 'FIX',...
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236 'forgettingFactor', lambda,...
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237 'show_dict', 1000);
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238
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239
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240 SMALL.DL(3) = SMALL_learn(SMALL.Problem, SMALL.DL(3));
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241
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242 % Initialising solver structure
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243 % Setting solver structure fields (toolbox, name, param, solution,
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244 % reconstructed and time) to zero values
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245
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246 SMALL.Problem.A = SMALL.DL(3).D;
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247 SMALL.Problem.reconstruct = @(x) ImageDenoise_reconstruct(x, SMALL.Problem);
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248
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249 SMALL.solver(3)=SMALL_init_solver;
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250
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251 % Defining the parameters needed for image denoising
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252
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253 SMALL.solver(3).toolbox='ompbox';
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254 SMALL.solver(3).name='omp2';
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255 SMALL.solver(3).param=struct(...
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256 'epsilon',Edata,...
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257 'maxatoms', maxatoms);
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258
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259
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260 SMALL.solver(3)=SMALL_solve(SMALL.Problem, SMALL.solver(3));
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261
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262 SMALL.solver(3).reconstructed.psnr
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263
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264
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265 % show results %
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266
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267 SMALL_ImgDeNoiseResult(SMALL);
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268
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269 results(noise_ind,im_num).psnr.ksvd=SMALL.solver(1).reconstructed.psnr;
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270 results(noise_ind,im_num).psnr.odct=SMALL.solver(2).reconstructed.psnr;
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271 results(noise_ind,im_num).psnr.rlsdla=SMALL.solver(3).reconstructed.psnr;
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272 results(noise_ind,im_num).vmrse.ksvd=SMALL.solver(1).reconstructed.vmrse;
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273 results(noise_ind,im_num).vmrse.odct=SMALL.solver(2).reconstructed.vmrse;
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274 results(noise_ind,im_num).vmrse.rlsdla=SMALL.solver(3).reconstructed.vmrse;
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275 results(noise_ind,im_num).ssim.ksvd=SMALL.solver(1).reconstructed.ssim;
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276 results(noise_ind,im_num).ssim.odct=SMALL.solver(2).reconstructed.ssim;
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277 results(noise_ind,im_num).ssim.rlsdla=SMALL.solver(3).reconstructed.ssim;
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278
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279 results(noise_ind,im_num).time.ksvd=SMALL.solver(1).time+SMALL.DL(1).time;
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280 results(noise_ind,im_num).time.rlsdla.time=SMALL.solver(3).time+SMALL.DL(3).time;
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281 clear SMALL;
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282 end
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283 end
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284 % save results.mat results
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