% 1D example
% TSVD deblur

% Build object
clear all, close all
t=[0:0.02:1]';
x=1*(t>0.25&t<0.75);

% Build blurring matrix and compute image
m=length(t);
c = zeros(m,1);
c(1:5) = [5:-1:1]'/25;
A = toeplitz(c);
b = A*x+0.01*randn(m,1);

% Plot object, image and naive solution.
[U,S,V]=svd(A);
alpha = input(' Truncation level = ');
Strunc = (S>alpha).*S;
xtsvd=V*pinv(Strunc)*U'*b;
figure(1)
  subplot(221)
    semilogy(diag(S))
    hold on, semilogy(alpha*ones(size(b)),'r'), hold off
    title('Singular Values of A')
  subplot(222)
    plot(U(:,1))
    title('Singular Vector 1')
  subplot(223)
    plot(U(:,5))
    title('Singular Vector 5')
  subplot(224)
    plot(U(:,25))
    title('Singular Vector 25')
    
figure(2)
  plot(t,x,'g-',t,b,'r--',t,xtsvd)
  axis([0 1 -0.5 1.5])
  legend('true','blurred','naive solution')