%  FWT_DB.M;
%  此示意程序用DWT實現二維小波變換
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clear;clc;
T=256;       %  圖像維數
SUB_T=T/2;   %  子圖維數
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%  1.調原始圖像矩陣
load wbarb;  %  下載圖像
f=X;         %  原始圖像
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%  2.進行二維小波分解
l=wfilters('db10','l');    %  db10（消失矩為10)低通分解濾波器沖擊響應（長度為20）
L=T-length(l);
l_zeros=[l,zeros(1,L)];    %  矩陣行數與輸入圖像一致，為2的整數冪
h=wfilters('db10','h');    %  db10（消失矩為10)高通分解濾波器沖擊響應（長度為20）
h_zeros=[h,zeros(1,L)];    %  矩陣行數與輸入圖像一致，為2的整數冪
for i=1:T;   %  列變換
    row(1:SUB_T,i)=dyaddown( ifft( fft(l_zeros).*fft(f(:,i)') ) ).';    %  圓周卷積<->FFT
    row(SUB_T+1:T,i)=dyaddown( ifft( fft(h_zeros).*fft(f(:,i)') ) ).';  %  圓周卷積<->FFT
end;
for j=1:T;   %  行變換
    line(j,1:SUB_T)=dyaddown( ifft( fft(l_zeros).*fft(row(j,:)) ) );    %  圓周卷積<->FFT
    line(j,SUB_T+1:T)=dyaddown( ifft( fft(h_zeros).*fft(row(j,:)) ) );  %  圓周卷積<->FFT
end;
decompose_pic=line;  %  分解矩陣
%  圖像分為四塊
lt_pic=decompose_pic(1:SUB_T,1:SUB_T);      %  在矩陣左上方為低頻分量--fi(x)*fi(y)
rt_pic=decompose_pic(1:SUB_T,SUB_T+1:T);    %  矩陣右上為--fi(x)*psi(y)
lb_pic=decompose_pic(SUB_T+1:T,1:SUB_T);    %  矩陣左下為--psi(x)*fi(y)
rb_pic=decompose_pic(SUB_T+1:T,SUB_T+1:T);  %  右下方為高頻分量--psi(x)*psi(y)
 
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%  3.分解結果顯示
figure(1);
colormap(map);
subplot(2,1,1);
image(f);  %  原始圖像  
title('original pic');
subplot(2,1,2);
image(abs(decompose_pic));  %  分解后圖像
title('decomposed pic');
figure(2);
colormap(map);
subplot(2,2,1);
image(abs(lt_pic));  %  左上方為低頻分量--fi(x)*fi(y)
title('\Phi(x)*\Phi(y)');
subplot(2,2,2);
image(abs(rt_pic));  %  矩陣右上為--fi(x)*psi(y)
title('\Phi(x)*\Psi(y)');
subplot(2,2,3);
image(abs(lb_pic));  %  矩陣左下為--psi(x)*fi(y)
title('\Psi(x)*\Phi(y)');
subplot(2,2,4);
image(abs(rb_pic));  %  右下方為高頻分量--psi(x)*psi(y)
title('\Psi(x)*\Psi(y)');
 
 
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%  5.重構源圖像及結果顯示
% construct_pic=decompose_matrix'*decompose_pic*decompose_matrix;
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l_re=l_zeros(end:-1:1);   %  重構低通濾波
l_r=circshift(l_re',1)';  %  位置調整
h_re=h_zeros(end:-1:1);   %  重構高通濾波
h_r=circshift(h_re',1)';  %  位置調整
 
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top_pic=[lt_pic,rt_pic];  %  圖像上半部分
t=0;
for i=1:T;  %  行插值低頻
 
    if (mod(i,2)==0)
        topll(i,:)=top_pic(t,:); %  偶數行保持
    else
        t=t+1;
        topll(i,:)=zeros(1,T);   %  奇數行為零
    end
end;
for i=1:T;  %  列變換
    topcl_re(:,i)=ifft( fft(l_r).*fft(topll(:,i)') )';  %  圓周卷積<->FFT
end;
 
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bottom_pic=[lb_pic,rb_pic];  %  圖像下半部分
t=0;
for i=1:T;  %  行插值高頻
    if (mod(i,2)==0)
        bottomlh(i,:)=bottom_pic(t,:);  %  偶數行保持
    else
        bottomlh(i,:)=zeros(1,T);       %  奇數行為零
        t=t+1;
    end
end;
for i=1:T; %  列變換
    bottomch_re(:,i)=ifft( fft(h_r).*fft(bottomlh(:,i)') )';  %  圓周卷積<->FFT
end;
 
construct1=bottomch_re+topcl_re;  %  列變換重構完畢
 
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left_pic=construct1(:,1:SUB_T);   %  圖像左半部分
t=0;
for i=1:T;  %  列插值低頻
 
    if (mod(i,2)==0)
        leftll(:,i)=left_pic(:,t); %  偶數列保持
    else
        t=t+1;
        leftll(:,i)=zeros(T,1);    %  奇數列為零
    end
end;
for i=1:T;  %  行變換
    leftcl_re(i,:)=ifft( fft(l_r).*fft(leftll(i,:)) );  %  圓周卷積<->FFT
end;
 
 
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right_pic=construct1(:,SUB_T+1:T);  %  圖像右半部分
t=0;
for i=1:T;  %  列插值高頻
    if (mod(i,2)==0)
        rightlh(:,i)=right_pic(:,t);  %  偶數列保持
    else
        rightlh(:,i)=zeros(T,1);      %  奇數列為零
        t=t+1;
    end
end;
for i=1:T; %  行變換
    rightch_re(i,:)=ifft( fft(h_r).*fft(rightlh(i,:)) );  %  圓周卷積<->FFT
end;
 
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construct_pic=rightch_re+leftcl_re;  %  重建全部圖像
 
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%  結果顯示
figure(3);
colormap(map);
subplot(2,1,1);
image(f);  %  源圖像顯示
title('original pic');
subplot(2,1,2);
image(abs(construct_pic));   %  重構源圖像顯示
title('reconstructed pic');
error=abs(construct_pic-f);  %  重構圖形與原始圖像誤值
figure(4);
mesh(error);  %  誤差三維圖像
title('absolute error display');