% Image compression example.

load clown.mat

A= X; colormap('gray')

[U,S,V] = svd(A);
[m n] = size(S);

Anew= zeros(m,n);
for k=1:10,
 Anew = Anew + S(k,k)*kron(U(:,k), V(:,k).');
end

Anew1= zeros(m,n);
for k=1:30,
 Anew1 = Anew1 + S(k,k)*kron(U(:,k), V(:,k).');
end

Anew2= zeros(m,n);
for k=1:80,
 Anew2 = Anew2 + S(k,k)*kron(U(:,k), V(:,k).');
end

%check the two norm error.
norm(A-Anew)/norm(A)
norm(A-Anew1)/norm(A)
norm(A-Anew2)/norm(A)

subplot(2,2,1)
image(A)

subplot(2,2,2);
image(Anew)

subplot(2,2,3)
image(Anew1)

subplot(2,2,4)
image(Anew2)