2代小波示意程序

from：http://waveletlegend.spaces.live.com/

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%%此程序用提升法实现第二代小波变换
%%我用的是非整数阶小波变换
%%采用时域实现,步骤先列后行
%%正变换：分裂，预测，更新；
%%反变换：更新，预测，合并
%%只做一层（可以多层，而且每层的预测和更新方程不同）
clear;clc;
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%1.调原始图像矩阵
loadwbarb;%下载图像
f=X;%原始图像
%f=[00000000;...
%00011000;...
%00244200;...
%01488410;...
%01488410;...
%00244200;...
%00011000;...
%00000000;];%原始图像矩阵
N=length(f);%图像维数
T=N/2;%子图像维数

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%%%%%%%%%%%%%%%%%正变换%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%1.列变换
%A.分裂（奇偶分开）
f1=f([1:2:N-1],:);%奇数
f2=f([2:2:N],:);%偶数
%f1(:,T+1)=f1(:,1);%补列
%f2(T+1,:)=f2(1,:);%补行
%B.预测
fori_hc=1:T;
high_frequency_column(i_hc,:)=f1(i_hc,:)-f2(i_hc,:);
end;
%high_frequency_column(T+1,:)=high_frequency_column(1,:);%补行
%C.更新
fori_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.行变换
%A.分裂（奇偶分开）
f1=f_column(:,[1:2:N-1]);%奇数
f2=f_column(:,[2:2:N]);%偶数

%f2(:,T+1)=f2(:,1);%补行
%B.预测
fori_hr=1:T;
high_frequency_row(:,i_hr)=f1(:,i_hr)-f2(:,i_hr);
end;
%high_frequency_row(:,T+1)=high_frequency_row(:,1);%补行
%C.更新
fori_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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%%%%%%%%%%%%%%%%%%%反变换%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%1.行变换
%A.提取（低频高频分开）
f1=f_row(:,[T+1:1:N]);%奇数
f2=f_row(:,[1:1:T]);%偶数

%f2(:,T+1)=f2(:,1);%补行
%B.更新
fori_lr=1:T;
low_frequency_row(:,i_lr)=f2(:,i_lr)-1/2*f1(:,i_lr);
end;
%C.预测
fori_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);%补行

%D.合并(奇偶分开合并)
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.列变换
%A.提取（低频高频分开）
f1=f_row([T+1:1:N],:);%奇数
f2=f_row([1:1:T],:);%偶数
%f1(:,T+1)=f1(:,1);%补列
%f2(T+1,:)=f2(1,:);%补行
%B.更新
fori_lc=1:T;
low_frequency_column(i_lc,:)=f2(i_lc,:)-1/2*f1(i_lc,:);
end;
%C.预测
fori_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,:);%补行

%D.合并(奇偶分开合并）
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);