2代小波示意程式
from:http://waveletlegend.spaces.live.com/
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%% 此程式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
%% 採用時域實現,步驟先列後行
%% 正變換:分裂,預測,更新;
%% 反變換:更新,預測,合併
%% 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.調原始影象矩陣
load wbarb; % 下載影象
f=X; % 原始影象
% 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 ;]; % 原始影象矩陣
N=length(f); % 影象維數
T=N/2; % 子影象維數
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%%%%%%%%%%%%%%%%%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.合併
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
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% 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.合併
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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%%%%%%%%%%%%%%%%%%%反變換%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%% 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
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% 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
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% D.合併(奇偶分開合併)
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);
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%%%% 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.合併(奇偶分開合併)
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);
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