2代小波示意程序此程序用提升法实现第二代小波变换用的是非整数阶小波变换

				2代小波示意程序 
				
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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; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
				%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
				%%%%
				
				%  1.调原始图像矩阵 load wbarb;  %  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   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
				%%%%%%%%%%%%%%%%%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);     
				%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
				%%%%%%%%%%%%%%%%%%%反变换%%%%%%%%%%%%%%%%%%%%%%%%%
				%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
				%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
				%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
				
				%%%%   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);