load gatlin                       % load the "gatlin" image data, built-in to MATLAB

% [U,S,V] = svd(X);                 % "gatlin" stores the image as the variable "X"
 
 figure(1),clf
 semilogy(diag(S),'b.','markersize',20)
 set(gca,'fontsize',16)
 title('singular values of the "gatlin" image matrix')
 xlabel('k'), ylabel('\sigma_k')

 figure(2),clf
 image(X), colormap(map)           % image: MATLAB command to display a matrix as image
 axis equal, axis off
 title('true image (rank 480)','fontsize',16)

 figure(3),clf
 k = 100;
 Xs = U(:,1:k)*S(1:k,1:k)*V(:,1:k)';
 image(Xs), colormap(map)
 axis equal, axis off
 title(sprintf('best rank-%d approximation',k),'fontsize',16)

 figure(4),clf
 k = 25;
 Xs = U(:,1:k)*S(1:k,1:k)*V(:,1:k)';
 image(Xs), colormap(map)
 axis equal, axis off
 title(sprintf('best rank-%d approximation',k),'fontsize',16)

 figure(5),clf
 k = 10;
 Xs = U(:,1:k)*S(1:k,1:k)*V(:,1:k)';
 image(Xs), colormap(map)
 axis equal, axis off
 title(sprintf('best rank-%d approximation',k),'fontsize',16)

 figure(6),clf
 k = 1;
 Xs = U(:,1:k)*S(1:k,1:k)*V(:,1:k)';
 image(Xs), colormap(map)
 axis equal, axis off
 title(sprintf('best rank-%d approximation',k),'fontsize',16)