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
load wbarb;  %  下载图像
f=X;         %  原始图像
% 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
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,:);  %  补行
%  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
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);  %  补行
%  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);
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%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
for i_lr=1:T;
    low_frequency_row(:,i_lr)=f2(:,i_lr)-1/2*f1(:,i_lr);
end;
%  C.预测
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);  %  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
for i_lc=1:T;
    low_frequency_column(i_lc,:)=f2(i_lc,:)-1/2*f1(i_lc,:);
end;
%  C.预测
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,:);  %  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);