%??此示意程序用DWT實現二維小波變換
%??編程人????沙威（Wei?Sha）?安徽大學（Anhui?University）?ws108@ahu.edu.cn

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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=[lzeros（1L）];????%??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=[hzeros（1L）];????%??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_Ti）=dyaddown（?ifft（?fft（l_zeros）.*fft（f（:i）‘）?）?）.‘;????%??圓周卷積<->FFT
????row（SUB_T+1:Ti）=dyaddown（?ifft（?fft（h_zeros）.*fft（f（:i）‘）?）?）.‘;??%??圓周卷積<->FFT
end;

for?j=1:T;???%??行變換
????line（j1:SUB_T）=dyaddown（?ifft（?fft（l_zeros）.*fft（row（j:））?）?）;????%??圓周卷積<->FFT
????line（jSUB_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_T1:SUB_T）;??????%??在矩陣左上方為低頻分量--fi（x）*fi（y）
rt_pic=decompose_pic（1:SUB_TSUB_T+1:T）;????%??矩陣右上為--fi（x）*psi（y）
lb_pic=decompose_pic（SUB_T+1:T1:SUB_T）;????%??矩陣左下為--psi（x）*fi（y）
rb_pic=decompose_pic（SUB_T+1:TSUB_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（211）;
image（f）;??%??原始圖像???
title（‘original?pic‘）;

subplot（212）;
image（abs（decompose_pic））;??%??分解后圖像
title（‘decomposed?pic‘）;?

figure（2）;
colormap（map）;

subplot（221）;
image（abs（lt_pic））;??%??左上方為低頻分量--fi（x）*fi（y）
title（‘\Phi（x）*\Phi（y）‘）;

subplot（222）;
image（abs（rt_pic））;??%??矩陣右上為--fi（x）*psi（y）
title（‘\Phi（x）*\Psi（y）‘）;

subplot（223）;
image（abs（lb_pic））;??%??矩陣左下為--psi（x）*fi（y）
title（‘\Psi（x）*\Phi（y）‘）;

subplot（224）;
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_picrt_pic];??%??圖像上半部分

t=0;
for?i=1:T;??%??行插值低頻
??
????if?（mod（i2）==0）
????????topll（i:）=top_pic（t:）;?%??偶數行保持
????else
????????t=t+1;
????????topll（i:）=zeros（1T）;???%??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_picrb_pic];??%??圖像下半部分

t=0;
for?i=1

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????1142??2018-09-18?16:33??DWT_1D.zip
?????文件????????5054??2007-06-12?10:46??DWT_2D.m
?????文件????????1599??2018-09-18?16:31??DWT_2D.zip