% DEMO_KPCADENOIS Idea of image denoising based on Kernel PCA.%% Description:%  The kernel PCA model is trained for to model input 2D vectors.%  The free model parameters (kernel argument, dimension) are %  tuned by the script train_kpca_denois. The denosing of corrupted %  vectors is based on projecting onto the kernel PCA model and %  take the resulting image as the reconstructed vector [Mika99b]. This %  idea is demonstrated on a toy 2D data. %  % See also %  GREEDYKPCA, KPCAREC, KPCA.%% About: Statistical Pattern Recognition Toolbox% (C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac% <a href="http://www.cvut.cz">Czech Technical University Prague</a>% <a href="http://www.feld.cvut.cz">Faculty of Electrical Engineering</a>% <a href="http://cmp.felk.cvut.cz">Center for Machine Perception</a>% Modifications:% 06-jun2004, VFhelp img_denois_idea;% setting %---------------------------------------% toy data generated by gencircledatainput_data_file = 'noisy_circle';  options.ker = 'rbf';  % kerneloptions.arg = 2;      % kernel argumentoptions.m = 500;      % #of vectors used for approximationoptions.p = 10;       % deth of search for the best basis vectoroptions.new_dim = 2;  % output dimensionoptions.verb = 1;   % load training data containing examples of corrupted and % corresponding ground truth vectors.load(input_data_file,'trn');[Dim,Num_Data] = size(trn.X);% train kernel PCAkpca_model = greedykpca(trn.X,options);% example of corrupted vector out of kernel PCA subspacecorr_x = [-2;4.5];% vector reconstructionrec_x = kpcarec(corr_x,kpca_model);% visualizationfigure; hold on; axis([-4 7 -4 7]);h0=ppatterns(trn.gnd_X,'r+');h1=ppatterns(trn.X,'gx');h3=ppatterns(rec_x,'bo',13);h2=ppatterns(corr_x,'mo',13);plot([rec_x(1) corr_x(1)],[rec_x(2) corr_x(2)],'k--');h4 = legend([h0 h1 h2 h3],'Ground truth','Noisy examples',...    'Corrupted','Reconstructed');set(h4,'FontSize',13);% EOF