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%% 本程序实现任意偶数大小图像第二代双正交97提升小波变换
%% 注1： 采用标准正交方法，对行列采用不同矩阵（和matlab里不同）
%% 注2： 为了保证正交，所有边界处理，全部采用循环处理
%% 注3： 正交性验证，将单位阵带入函数，输出仍是单位阵（matlab不具有此性质）
%% 注4： 此程序是矩阵实现，所以图像水平分量和垂直分量估计被交换位置
%% 注5： 此程序实现的是类小波（wavelet-like）变换，是介于小波包变换与小波变换之间的变换
%% 注6： 此程序每层变换相对原图像矩阵，产生的矩阵都是正交阵，这和小波包一致
%% 注7： 但小波变换每层产生的矩阵，是相对每个待分解子块的正交矩阵，而不是原图像的正交矩阵
%% 注8： 且小波变换产生的正交矩阵维数，随分解层数2分减少
%% 注9: 提升系数可以在MATLAB7.0以上版本，用liftwave('9.7')获取，这里直接给出，考虑兼容性
%% 注10：由于MATLAB数组下标从1开始，所以注意奇偶序列的变化
%% 注11：d为对偶上升，即预测；p为原上升，即更新
%% x输入图像,y输出图像
%% flag_trans为正变换或反变换标志，0执行正变换，1执行反变换
%% flag_max,是否最大层数变换标志,0执行用户设定层数,1执行最大层数变换
%% layer,用户层数设置（小于最大层）
function y=db97(x,flag_trans,flag_max,layer);
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% 1.输入参数检查
% 矩阵维数判断
[sa,sb]=size(x);
if (sa~=sb) % 防止非图像数据
errordlg('非图像数据！');
error('非图像数据！');
end;
% 变换标志判断
[sa,sb]=size(flag_trans);
if ((sa~=1) | (sb~=1)) % 变换标志错误
errordlg('变换标志错误！');
error('变换标志错误！');
end;
if ((flag_trans~=1) & (flag_trans~=0)) % 变换标志错误
errordlg('变换标志错误！');
error('变换标志错误！');
end;
% 最大层数标志判断
[sa,sb]=size(flag_max);
if ((sa~=1) | (sb~=1)) % 最大层数标志错误
errordlg('最大层数标志错误！');
error('最大层数标志错误！');
end;
if ((flag_max~=1) & (flag_max~=0)) % 最大层数标志错误
errordlg('最大层数标志错误！');
error('最大层数标志错误！');
end;
% 用户设置层数判断
if (flag_max~=1)
[sa,sb]=size(layer);
if ((sa~=1) | (sb~=1)) % 层数设置错误
errordlg('层数设置错误！');
error('层数设置错误！');
end;
if (flag_max<0) % 层数设置错误
errordlg('层数设置错误！');
error('层数设置错误！');
end;
end;
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% 2.提升系数确定
% t1=liftwave('9.7'); % 获取提升系数(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.分解层数确定
% 采用用户输入和自动给出最大层数两种方法
N=length(x); % 矩阵大小
S=N; % 变量
s=log2(N); % 最大循环次数
n1=N/2; % 初始一半矩阵大小
n2=N; % 初始矩阵大小
u=0; % 初始值
% 对非2的整数幂大小图像确定最大分解层数
for ss=1:s
if (mod(S,2)==0)
u=u+1;
S=S/2;
end;
end;
u=u-1; % 分解最大层数减1(后面的边界处理造成)
% 最大层数确定
if (flag_max==0) % 手动输入
T=layer; % 用户输入值
else % 自动确定最大层数
T=u; % 分解最大层数
end
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% 4.最大层数和图像大小检查
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% 5.提升法正变换
if (flag_trans==0)
for time=1:T;
% 行正变换
% 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],:);
% 归一
x([1:n1],:)=p3*x([1:n1],:);
x([n1+1:n2],:)=d3*x([n1+1:n2],:);
clear x1;
% 列正变换
% 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]);
% 归一
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.提升法反变换
else
n2=N/(2.^(T-1)); % 分解最小子块维数
n1=n2/2;
for time=1:T;
% 行反变换
% 去归一
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],:);
% 偶数
x([1:2:n2-1],:)=x1([1:n1],:);
clear x1;
% 列反变换
% 归一
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.结果输出
y=x; % 传输最后结果
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% 8.内存清理
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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