提升法97經(jīng)典程序
%%  本程序?qū)崿F(xiàn)任意偶數(shù)大小圖像第二代雙正交97提升小波變換
%%  注1： 采用標準正交方法，對行列采用不同矩陣（和matlab里不同）
%%  注2： 為了保證正交，所有邊界處理，全部采用循環(huán)處理
%%  注3： 正交性驗證，將單位陣帶入函數(shù)，輸出仍是單位陣（matlab不具有此性質(zhì)）
%%  注4： 此程序是矩陣實現(xiàn)，所以圖像水平分量和垂直分量估計被交換位置
%%  注5： 此程序?qū)崿F(xiàn)的是類小波（wavelet-like）變換，是介于小波包變換與小波變換之間的變換
%%  注6： 此程序每層變換相對原圖像矩陣，產(chǎn)生的矩陣都是正交陣，這和小波包一致
%%  注7： 但小波變換每層產(chǎn)生的矩陣，是相對每個待分解子塊的正交矩陣，而不是原圖像的正交矩陣
%%  注8： 且小波變換產(chǎn)生的正交矩陣維數(shù)，隨分解層數(shù)2分減少
%%  注9:  提升系數(shù)可以在MATLAB7.0以上版本，用liftwave('9.7')獲取，這里直接給出，考慮兼容性
%%  注10：由于MATLAB數(shù)組下標從1開始，所以注意奇偶序列的變化
%%  注11：d為對偶上升，即預(yù)測；p為原上升，即更新
%%  編程人  沙威 安徽大學
%%  編程時間  2004年12月18日
%%  x輸入圖像,y輸出圖像
%%  flag_trans為正變換或反變換標志，0執(zhí)行正變換，1執(zhí)行反變換
%%  flag_max,是否最大層數(shù)變換標志,0執(zhí)行用戶設(shè)定層數(shù),1執(zhí)行最大層數(shù)變換
%%  layer,用戶層數(shù)設(shè)置（小于最大層）
function y=db97(x,flag_trans,flag_max,layer);
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%  1.輸入?yún)?shù)檢查
%  矩陣維數(shù)判斷
[sa,sb]=size(x);
if (sa~=sb)       %  防止非圖像數(shù)據(jù)
    errordlg('非圖像數(shù)據(jù)！');
    error('非圖像數(shù)據(jù)！');
end;
%  變換標志判斷
[sa,sb]=size(flag_trans);
if ((sa~=1) | (sb~=1))                  %  變換標志錯誤
    errordlg('變換標志錯誤！');
    error('變換標志錯誤！');
end;
if ((flag_trans~=1) & (flag_trans~=0))  %  變換標志錯誤
    errordlg('變換標志錯誤！');
    error('變換標志錯誤！');
end;
%  最大層數(shù)標志判斷
[sa,sb]=size(flag_max);
if ((sa~=1) | (sb~=1))              %  最大層數(shù)標志錯誤
    errordlg('最大層數(shù)標志錯誤！');
    error('最大層數(shù)標志錯誤！');
end;
if ((flag_max~=1) & (flag_max~=0))  %  最大層數(shù)標志錯誤
    errordlg('最大層數(shù)標志錯誤！');
    error('最大層數(shù)標志錯誤！');
end;
%  用戶設(shè)置層數(shù)判斷
if (flag_max~=1)
    [sa,sb]=size(layer);
    if ((sa~=1) | (sb~=1))       %  層數(shù)設(shè)置錯誤
        errordlg('層數(shù)設(shè)置錯誤！');
        error('層數(shù)設(shè)置錯誤！');
    end;
    if (flag_max<0)              %  層數(shù)設(shè)置錯誤
        errordlg('層數(shù)設(shè)置錯誤！');
        error('層數(shù)設(shè)置錯誤！');
    end;
end;
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%  2.提升系數(shù)確定
%  t1=liftwave('9.7');  %  獲取提升系數(shù)(MATLAB7.0以后)
d1=[-1.586100000000000e+000,-1.586134342069360e+000];
p1=[1.079600000000000e+000,-5.298011857188560e-002];
d2=[-8.829110755411875e-001,-8.829110755411875e-001];
p2=[4.435068520511142e-001,1.576123746148364e+000];
d3=-8.698644516247808e-001;
p3=-1.149604398860242e+000;
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%  3.分解層數(shù)確定
%  采用用戶輸入和自動給出最大層數(shù)兩種方法
N=length(x); %  矩陣大小
S=N;         %  變量
s=log2(N);   %  最大循環(huán)次數(shù)
n1=N/2;      %  初始一半矩陣大小
n2=N;        %  初始矩陣大小
u=0;         %  初始值
%  對非2的整數(shù)冪大小圖像確定最大分解層數(shù)
for ss=1:s
    if (mod(S,2)==0)
        u=u+1;
        S=S/2;
    end;
end;
u=u-1;            %  分解最大層數(shù)減1(后面的邊界處理造成)
%  最大層數(shù)確定
if (flag_max==0)  %  手動輸入
    T=layer;      %  用戶輸入值
else              %  自動確定最大層數(shù)
    T=u;          %  分解最大層數(shù)
end
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%  4.最大層數(shù)和圖像大小檢查
if (T>u)          %  防止用戶層數(shù)越界
    errordlg('已超過最大分解層數(shù)！或者非偶數(shù)大小圖像！');
    error('已超過最大分解層數(shù)！或者非偶數(shù)大小圖像！');
end;
if (mod(N,2)~=0)  %  防止圖像大小錯誤
    errordlg('非偶數(shù)大小圖像！');
    error('非偶數(shù)大小圖像！');
end;

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%  5.提升法正變換
if (flag_trans==0)
    for time=1:T;
        %  行正變換
        
        % d;
        x1(n1,:)=x(n2,:)+d1(2)*x(n2-1,:)+d1(1)*x(1,:);  
        x1([1:n1-1],:)=x([2:2:n2-2],:)+d1(2)*x([1:2:n2-3],:)+d1(1)*x([3:2:n2-1],:); 
        
        % p;
        x(1,:)=x(1,:)+p1(2)*x1(n1,:)+p1(1)*x1(1,:); 
        x([2:n1],:)=x([3:2:n2-1],:)+p1(2)*x1([1:n1-1],:)+p1(1)*x1([2:n1],:); 
        x([n1+1:n2],:)=x1([1:n1],:);
 
        % d;        
        x(n1+1,:)=x(n1+1,:)+d2(2)*x(n1,:)+d2(1)*x(1,:);
        x([n1+2:n2],:)=x([n1+2:n2],:)+d2(2)*x([1:n1-1],:)+d2(1)*x([2:n1],:);
        
        % p;
        x(n1,:)=x(n1,:)+p2(2)*x(n1+1,:)+p2(1)*x(n1+2,:);
        x(n1-1,:)=x(n1-1,:)+p2(2)*x(n2,:)+p2(1)*x(n1+1,:);
        x([1:n1-2],:)=x([1:n1-2],:)+p2(2)*x([n1+2:n2-1],:)+p2(1)*x([n1+3:n2],:);
        
        % 歸一
        x([1:n1],:)=p3*x([1:n1],:);
        x([n1+1:n2],:)=d3*x([n1+1:n2],:);
        clear x1;
        
        %  列正變換
        
        % d;
        x1(:,[1:n1])=x(:,[2:2:n2]);
        
        % p;
        x(:,1)=x(:,1)-d1(1)*x1(:,n1)-d1(2)*x1(:,1);  
        x(:,[2:n1])=x(:,[3:2:n2-1])-d1(1)*x1(:,[1:n1-1])-d1(2)*x1(:,[2:n1]); 
        x(:,[n1+1:n2])=x1(:,[1:n1]);
        
        % d;
        x(:,n2)=x(:,n2)-p1(1)*x(:,n1)-p1(2)*x(:,1);
        x(:,[n1+1:n2-1])=x(:,[n1+1:n2-1])-p1(1)*x(:,[1:n1-1])-p1(2)*x(:,[2:n1]);
 
        % p;        
        x(:,n1,:)=x(:,n1)-d2(1)*x(:,n2)-d2(2)*x(:,n1+1);
        x(:,[1:n1-1])=x(:,[1:n1-1])-d2(1)*x(:,[n1+1:n2-1])-d2(2)*x(:,[n1+2:n2]);
        
        % d;
        x(:,n1+1)=x(:,n1+1)-p2(1)*x(:,n1-1)-p2(2)*x(:,n1);
        x(:,n1+2)=x(:,n1+2)-p2(1)*x(:,n1)-p2(2)*x(:,1);
        x(:,[n1+3:n2])=x(:,[n1+3:n2])-p2(1)*x(:,[1:n1-2])-p2(2)*x(:,[2:n1-1]);
        
        % 歸一
        x(:,[1:n1])=d3*x(:,[1:n1]);
        x(:,[n1+1:n2])=p3*x(:,[n1+1:n2]);
        clear x1;
        
        n2=n2/2; %  原大小
        n1=n2/2; %  一半大小
     end;

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%  6.提升法反變換
else
    n2=N/(2.^(T-1)); %  分解最小子塊維數(shù)
    n1=n2/2;
    for time=1:T;
        %  行反變換
        
        %  去歸一
        x([1:n1],:)=x([1:n1],:)/p3;
        x([n1+1:n2],:)=x([n1+1:n2],:)/d3;
        %  反p;
        x(n1,:)=x(n1,:)-p2(2)*x(n1+1,:)-p2(1)*x(n1+2,:);
        x(n1-1,:)=x(n1-1,:)-p2(2)*x(n2,:)-p2(1)*x(n1+1,:);
        x([1:n1-2],:)=x([1:n1-2],:)-p2(2)*x([n1+2:n2-1],:)-p2(1)*x([n1+3:n2],:);
        
        %  反d;        
        x(n1+1,:)=x(n1+1,:)-d2(2)*x(n1,:)-d2(1)*x(1,:);
        x([n1+2:n2],:)=x([n1+2:n2],:)-d2(2)*x([1:n1-1],:)-d2(1)*x([2:n1],:);
        
        %  反p;
        x1(1,:)=x(1,:)-p1(2)*x(n2,:)-p1(1)*x(n1+1,:); 
        x1([2:n1],:)=x([2:n1],:)-p1(2)*x([n1+1:n2-1],:)-p1(1)*x([n1+2:n2],:); 
       
        %  反d;
        x(n2,:)=x(n2,:)-d1(2)*x1(n1,:)-d1(1)*x1(1,:);  
        x([2:2:n2-2],:)=x([n1+1:n2-1],:)-d1(2)*x1([1:n1-1],:)-d1(1)*x1([2:n1],:); 
        
        %  偶數(shù) 
        x([1:2:n2-1],:)=x1([1:n1],:);
        
        clear x1;
        
        %  列反變換
        
        %  歸一
        x(:,[1:n1])=x(:,[1:n1])/d3;
        x(:,[n1+1:n2])=x(:,[n1+1:n2])/p3;
        %  反d;
        x(:,n1+1)=x(:,n1+1)+p2(1)*x(:,n1-1)+p2(2)*x(:,n1);
        x(:,n1+2)=x(:,n1+2)+p2(1)*x(:,n1)+p2(2)*x(:,1);
        x(:,[n1+3:n2])=x(:,[n1+3:n2])+p2(1)*x(:,[1:n1-2])+p2(2)*x(:,[2:n1-1]);
        
        %  反p;        
        x(:,n1,:)=x(:,n1)+d2(1)*x(:,n2)+d2(2)*x(:,n1+1);
        x(:,[1:n1-1])=x(:,[1:n1-1])+d2(1)*x(:,[n1+1:n2-1])+d2(2)*x(:,[n1+2:n2]);
        
        %  反d;
        x(:,n2)=x(:,n2)+p1(1)*x(:,n1)+p1(2)*x(:,1);
        x(:,[n1+1:n2-1])=x(:,[n1+1:n2-1])+p1(1)*x(:,[1:n1-1])+p1(2)*x(:,[2:n1]);
        
        %  反p;
        x1(:,1)=x(:,1)+d1(1)*x(:,n2)+d1(2)*x(:,n1+1);  
        x1(:,[2:n1])=x(:,[2:n1])+d1(1)*x(:,[n1+1:n2-1])+d1(2)*x(:,[n1+2:n2]); 
        %  奇偶
        x(:,[2:2:n2])=x(:,[n1+1:n2]);
        x(:,[1:2:n2-1])=x1(:,[1:n1]);
        clear x1;
        
        n2=n2*2; %  原大小
        n1=n2/2; %  一半大小
    end;
end;
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%  7.結(jié)果輸出
y=x;  %  傳輸最后結(jié)果
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%  8.內(nèi)存清理
clear x;
clear flag_max;
clear layer;
clear flag_trans;
clear N;
clear n1;
clear n2;
clear s;
clear ss;
clear u;
clear d1;
clear d2;
clear d3;
clear p1;
clear p2;
clear p3;
clear sa;
clear sb;
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