第二代提升法实现的小波变换程序

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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）=h