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1 clc, clear, close all
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2
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3 %% Parameteres
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4 nTrials = 10; %number of trials of the experiment
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5
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6 % Dictionary learning parameters
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7 toolbox = 'TwoStepDL'; %dictionary learning toolbox
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8 dicUpdate = 'ksvd'; %dictionary learning updates
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9 dicDecorr = {'iterproj','ink-svd','shrinkgram'}; %dictionary decorrelation methods
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10 minCoherence = linspace(0.1,1,10); %coherence levels
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11
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12 iterNum = 20; %number of iterations
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13 epsilon = 1e-6; %tolerance level
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14 dictSize = 512; %number of atoms in the dictionary
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15 percActiveAtoms = 5; %percentage of active atoms
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16
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17 % Test signal parameters
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18 signal = audio('music03_16kHz.wav'); %audio signal
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19 blockSize = 256; %size of audio frames
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20 overlap = 0.5; %overlap between consecutive frames
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21
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22 % Dependent parameters
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23 nActiveAtoms = fix(blockSize/100*percActiveAtoms); %number of active atoms
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24
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25 % Initial dictionaries
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26 gaborParam = struct('N',blockSize,'redundancyFactor',2,'wd',@rectwin);
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27 gaborDict = Gabor_Dictionary(gaborParam);
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28 initDicts = {[],gaborDict};
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29
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30 %% Generate audio approximation problem
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31 signal = buffer(signal,blockSize,blockSize*overlap,@rectwin); %buffer frames of audio into columns of the matrix S
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32 SMALL.Problem.b = signal.S;
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33 SMALL.Problem.b1 = SMALL.Problem.b; % copy signals from training set b to test set b1 (needed for later functions)
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34
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35 % omp2 sparse representation solver
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36 ompParam = struct('X',SMALL.Problem.b,'epsilon',epsilon,'maxatoms',nActiveAtoms); %parameters
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37 solver = SMALL_init_solver('ompbox','omp2',ompParam,false); %solver structure
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38
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39
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40 %% Test
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41 nDecorrAlgs = length(dicDecorr); %number of decorrelation algorithms
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42 nCorrLevels = length(minCoherence); %number of coherence levels
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43 nInitDicts = length(initDicts); %number of initial dictionaries
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44
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45 SMALL.DL(nTrials,nInitDicts,nCorrLevels,nDecorrAlgs) = SMALL_init_DL(toolbox); %create dictionary learning structures
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46 for iTrial=1:nTrials
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47 for iInitDicts=1:nInitDicts
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48 for iCorrLevels=1:nCorrLevels
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49 for iDecorrAlgs=1:nDecorrAlgs
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50 SMALL.DL(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs).toolbox = toolbox;
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51 SMALL.DL(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs).name = dicUpdate;
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52 SMALL.DL(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs).profile = true;
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53 SMALL.DL(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs).param = ...
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54 struct( 'data',SMALL.Problem.b,...
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55 'Tdata',nActiveAtoms,...
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56 'dictsize',dictSize,...
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57 'iternum',iterNum,...
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58 'memusage','high',...
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59 'solver',solver,...
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60 'decFcn',dicDecorr{iDecorrAlgs},...
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61 'coherence',minCoherence(iCorrLevels),...
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62 'initdict',initDicts(iInitDicts));
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63
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64 SMALL.DL(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs) = ...
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65 SMALL_learn(SMALL.Problem,SMALL.DL(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs));
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66 save('SMALL_DL','SMALL');
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67 end
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68 end
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69 end
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70 end
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71
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72 %% Evaluate coherence and snr of representation for the various methods
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73 sr = zeros(size(SMALL.DL)); %signal to noise ratio
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74 mu = zeros(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs,blockSize); %cumulative coherence
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75 dic(size(SMALL.DL)) = dictionary; %initialise dictionary objects
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76 for iTrial=1:nTrials
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77 for iInitDicts=1:nInitDicts
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78 for iCorrLevels=1:nCorrLevels
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79 for iDecorrAlgs=1:nDecorrAlgs
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80 %Sparse representation
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81 SMALL.Problem.A = SMALL.DL(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs).D;
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82 tempSolver = SMALL_solve(SMALL.Problem,solver);
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83 %calculate snr
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84 sr(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs) = ...
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85 snr(SMALL.Problem.b,SMALL.DL(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs).D*tempSolver.solution);
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86 %calculate mu
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87 dic(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs) = ...
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88 dictionary(SMALL.DL(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs).D);
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89 mu(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs,:) = ...
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90 dic(iTrial,iInitDicts,iCorrLevels,iDecorrAlgs).cumcoherence;
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91 end
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92 end
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93 end
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94 end
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95
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96 %% Plot results
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97 minMu = sqrt((dictSize-blockSize)/(blockSize*(dictSize-1))); %lowe bound on coherence
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98 initDictsNames = {'Data','Gabor'};
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99 dicDecorrNames = {'Iter. Proj. + Rotation','INK-SVD','Iter. Proj.'};
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100 lineStyles = {'ks-','kd-','ko-'};
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101 for iInitDict=1:nInitDicts
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102 figure, hold on, grid on
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103 title([initDictsNames{iInitDict} ' Initialisation']);
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104 plot([1 1],[0 25],'k-');
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105 for iDecorrAlgs=1:nDecorrAlgs
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106 plot(mu(1,iInitDict,:,iDecorrAlgs,1),sr(1,iInitDict,:,iDecorrAlgs),...
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107 lineStyles{iDecorrAlgs});
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108 end
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109 plot([minMu minMu],[0 25],'k--')
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110
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111 set(gca,'YLim',[0 25],'XLim',[0 1.4]);
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112 legend([{'\mu_{max}'},dicDecorrNames,{'\mu_{min}'}]);
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113 xlabel('\mu');
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114 ylabel('SNR (dB)');
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115 end
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