% TRAIN_LIN_DENOIS Training of linear PCA model for image denoising.
%
% Description:
% The linear PCA model is trained to describe an input
% class of images corrupted by noise. The training data
% contains images corrupted by noise and corresponding
% ground truth. The output dimension of the linear PCA
% is tuned by cross-validation. The objective function
% is a sum of squared differences between ground truth
% images and reconstructed images.
%
% See also
% PCA, PCAREC, LINPROJ.
%
% 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:
% 07-jun-2004, VF
% 05-may-2004, VF
% 17-mar-2004, VF
num_folds = 1;
New_Dim_Range = [1 2];
input_data_file = 'noisy_circle';
output_data_file = [];
load(input_data_file,'trn','tst');
[Dim,num_data] = size( trn.X );
[itrn,itst]=crossval(num_data,num_folds);
Mse = [];
for new_dim = New_Dim_Range,
fprintf('\nnew_dim = %d\n', new_dim);
cv_mse = 0;
for i=1:num_folds,
fprintf('\n');
trn_X = trn.gnd_X(:,itrn{i});
val_gnd_X = trn.gnd_X(:,itst{i});
val_corr_X = trn.X(:,itst{i});
fprintf('Computing Linear PCA...');
lin_model = pca(trn_X, new_dim);
fprintf('done\n');
fprintf('Projecting validation data...');
val_reconst_X = pcarec( val_corr_X, lin_model );
fprintf('done.\n');
dummy = (val_reconst_X - val_gnd_X).^2;
mse = sum(dummy(:))/size(val_gnd_X,2);
fprintf('folder %d/%d: validation errors mse=%f\n', ...
i, num_folds, mse);
cv_mse = cv_mse + mse;
end
cv_mse = cv_mse/num_folds;
Mse(find(new_dim==New_Dim_Range)) = cv_mse;
fprintf('new_dim = %d: mse = %f\n', new_dim, cv_mse);
end
[dummy,inx] = min(Mse);
fprintf('\nMin(mse) = %f, dim = %f\n', ...
Mse(inx), New_Dim_Range(inx) );
fprintf('Computing optimal Kernel PCA...');
lpca_model = pca( trn.X, New_Dim_Range(inx) );
fprintf('done.\n');
if isempty(output_data_file),
figure; hold on;
xlabel('dim'); ylabel('mse');
plot(New_Dim_Range,Mse);
else
save(output_data_file,'New_Dim_Range',...
'Mse','num_folds','input_data_file',...
'output_data_file','lpca_model');
end
if Dim == 2 & isempty(output_data_file),
X = pcarec(tst.X, lin_model );
mse = sum(sum((X-tst.gnd_X).^2 ));
fprintf('\ntest mse=%f\n', mse);
figure; hold on;
h0=ppatterns(tst.gnd_X,'r+');
h1=ppatterns(tst.X,'gx');
h2=ppatterns(X,'bo');
legend([h0 h1 h2],'Ground truth','Noisy','Reconst');
end