第二代小波变换源码
%%第二代小波变换源码%% 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;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% 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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%正变换%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% 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);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% 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);
