function [I_W , S] = func_DWT(I, level, type);
%
% Wavelet decomposition
%
% input:    I : input image
%           level : wavelet decomposition level
%           type : wavelet used for the decomposition
%
% output:   I_W : decomposed image vector
%           S : corresponding bookkeeping matrix
% This code is by Jing Tian
%

[C,S] = func_Mywavedec2(I,level,type); 

S(:,3) = S(:,1).*S(:,2);        % dim of detail coef nmatrices

L = length(S);

I_W = zeros(S(L,1),S(L,2));

% approx part
I_W( 1:S(1,1) , 1:S(1,2) ) = reshape(C(1:S(1,3)),S(1,1:2));

for k = 2 : L-1
    rows = [sum(S(1:k-1,1))+1:sum(S(1:k,1))];
    columns = [sum(S(1:k-1,2))+1:sum(S(1:k,2))];
    % horizontal part
    c_start = S(1,3) + 3*sum(S(2:k-1,3)) + 1;
    c_stop = S(1,3) + 3*sum(S(2:k-1,3)) + S(k,3);
    I_W( 1:S(k,1) , columns ) = reshape( C(c_start:c_stop) , S(k,1:2) );

    % vertical part
    c_start = S(1,3) + 3*sum(S(2:k-1,3)) + S(k,3) + 1;
    c_stop = S(1,3) + 3*sum(S(2:k-1,3)) + 2*S(k,3);
    I_W( rows , 1:S(k,2) ) = reshape( C(c_start:c_stop) , S(k,1:2) );

    % diagonal part
    c_start = S(1,3) + 3*sum(S(2:k-1,3)) + 2*S(k,3) + 1;
    c_stop = S(1,3) + 3*sum(S(2:k,3));
    I_W( rows , columns ) = reshape( C(c_start:c_stop) , S(k,1:2) );

end