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%%  此程序用提升法實現第二代小波變換
%%  我用的是非整數階小波變換
%%  采用時域實現,步驟先列后行
%%  正變換：分裂，預測，更新；
%%  反變換：更新，預測，合并
%%  只做一層（可以多層，而且每層的預測和更新方程不同）

clear;clc;

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%%%%%  1.調原始圖像矩陣

load wbarb;  %  下載圖像
f=X;         %  原始圖像
% f=[0 0 0 0 0 0 0 0 ;...
%    0 0 0 1 1 0 0 0 ;...
%    0 0 2 4 4 2 0 0 ;...
%    0 1 4 8 8 4 1 0 ;...
%    0 1 4 8 8 4 1 0 ;...
%    0 0 2 4 4 2 0 0 ;...
%    0 0 0 1 1 0 0 0 ;...
%    0 0 0 0 0 0 0 0 ;];  %  原始圖像矩陣

N=length(f);         %  圖像維數
T=N/2;               %  子圖像維數



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%%%%%%%%%%%%%%%%%正變換%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%   1.列變換

%  A.分裂（奇偶分開）

f1=f([1:2:N-1],:);  %  奇數
f2=f([2:2:N],:);    %  偶數

% f1(:,T+1)=f1(:,1);  %  補列
% f2(T+1,:)=f2(1,:);  %  補行

%  B.預測

for i_hc=1:T;
    high_frequency_column(i_hc,:)=f1(i_hc,:)-f2(i_hc,:);
end;

% high_frequency_column(T+1,:)=high_frequency_column(1,:);  %  補行

%  C.更新

for i_lc=1:T;
    low_frequency_column(i_lc,:)=f2(i_lc,:)+1/2*high_frequency_column(i_lc,:);
end;

%  D.合并
f_column([1:1:T],:)=low_frequency_column([1:T],:);
f_column([T+1:1:N],:)=high_frequency_column([1:T],:);
    
    
figure(1)
colormap(map);
image(f);

figure(2)
colormap(map);
image(f_column);


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%%%%   2.行變換

%  A.分裂（奇偶分開）

f1=f_column(:,[1:2:N-1]);  %  奇數
f2=f_column(:,[2:2:N]);    %  偶數


% f2(:,T+1)=f2(:,1);    %  補行

%  B.預測

for i_hr=1:T;
    high_frequency_row(:,i_hr)=f1(:,i_hr)-f2(:,i_hr);
end;

% high_frequency_row(:,T+1)=high_frequency_row(:,1);  %  補行

%  C.更新

for i_lr=1:T;
    low_frequency_row(:,i_lr)=f2(:,i_lr)+1/2*high_frequency_row(:,i_lr);
end;

%  D.合并
f_row(:,[1:1:T])=low_frequency_row(:,[1:T]);
f_row(:,[T+1:1:N])=high_frequency_row(:,[1:T]);
    

figure(3)
colormap(map);
image(f_row);





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%%%%%%%%%%%%%%%%%%%反變換%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%   1.行變換

%   A.提取（低頻高頻分開）

f1=f_row(:,[T+1:1:N]);  %  奇數
f2=f_row(:,[1:1:T]);    %  偶數


% f2(:,T+1)=f2(:,1);    %  補行

%  B.更新

for i_lr=1:T;
    low_frequency_row(:,i_lr)=f2(:,i_lr)-1/2*f1(:,i_lr);
end;

%  C.預測

for i_hr=1:T;
    high_frequency_row(:,i_hr)=f1(:,i_hr)+low_frequency_row(:,i_hr);
end;

% high_frequency_row(:,T+1)=high_frequency_row(:,1);  %  補行


%  D.合并(奇偶分開合并)
f_row(:,[2:2:N])=low_frequency_row(:,[1:T]);
f_row(:,[1:2:N-1])=high_frequency_row(:,[1:T]);
    

figure(4)
colormap(map);
image(f_row);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%   2.列變換

%  A.提取（低頻高頻分開）

f1=f_row([T+1:1:N],:);  %  奇數
f2=f_row([1:1:T],:);    %  偶數

% f1(:,T+1)=f1(:,1);  %  補列
% f2(T+1,:)=f2(1,:);  %  補行

%  B.更新

for i_lc=1:T;
    low_frequency_column(i_lc,:)=f2(i_lc,:)-1/2*f1(i_lc,:);
end;

%  C.預測

for i_hc=1:T;
    high_frequency_column(i_hc,:)=f1(i_hc,:)+low_frequency_column(i_hc,:);
end;

% high_frequency_column(T+1,:)=high_frequency_column(1,:);  %  補行



%  D.合并(奇偶分開合并）
f_column([2:2:N],:)=low_frequency_column([1:T],:);
f_column([1:2:N-1],:)=high_frequency_column([1:T],:);
    
    
figure(5)
colormap(map);
image(f_column);