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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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%%%%???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）=h