2代小波示意程序 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  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;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%  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
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%正變換%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%   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);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%   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);
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%反變換%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%   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);