2代小波示意程序

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CODE:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 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; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%

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