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 = [ 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);


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%%%%%%%%%%%%%%%%%%% 反变换 %%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% 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);