matlab 二维小波变换程序
| MATLAB2维小波变换经典程序 |
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% FWT_DB.M;
% 此示意程序用DWT实现二维小波变换 % 编程时间2004-4-10，编程人沙威
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%% clear;clc;
T=256; % 图像维数
SUB_T=T/2; % 子图维数
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1.调原始图像矩阵
load wbarb; % 下载图像
f=X; % 原始图像
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 2.进行二维小波分解
l=wfilters('db10','l'); % db10（消失矩为10)低通分解滤波器冲击响应（长度为20）
L=T-length(l); l_zeros=[l,zeros(1,L)]; % 矩阵行数与输入图像一致，为2的整数幂
h=wfilters('db10','h'); % db10（消失矩为10)高通分解滤波器冲击响应（长度为20）
h_zeros=[h,zeros(1,L)]; % 矩阵行数与输入图像一致，为2的整数幂
for i=1:T; % 列变换
row(1:SUB_T,i)=dyaddown( ifft( fft(l_zeros).*fft(f(:,i)') ) ).'; % 圆周卷积<->FFT row(SUB_T+1:T,i)=dyaddown( ifft( fft(h_zeros).*fft(f(:,i)') ) ).'; % 圆周卷积<->FFT end;
for j=1:T; % 行变换
line(j,1:SUB_T)=dyaddown( ifft( fft(l_zeros).*fft(row(j,:)) ) ); % 圆周卷积<->FFT line(j,SUB_T+1:T)=dyaddown( ifft( fft(h_zeros).*fft(row(j,:)) ) ); % 圆周卷积<->FFT end;
decompose_pic=line; % 分解矩阵
% 图像分为四块
lt_pic=decompose_pic(1:SUB_T,1:SUB_T); % 在矩阵左上方为低频分量--fi(x)*fi(y)
rt_pic=decompose_pic(1:SUB_T,SUB_T+1:T); % 矩阵右上为--fi(x)*psi(y) lb_pic=decompose_pic(SUB_T+1:T,1:SUB_T); % 矩阵左下为--psi(x)*fi(y) rb_pic=decompose_pic(SUB_T+1:T,SUB_T+1:T); % 右下方为高频分量--psi(x)*psi(y)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 3.分解结果显示
figure(1);
colormap(map);
subplot(2,1,1);
image(f); % 原始图像 title('original pic');
subplot(2,1,2);
image(abs(decompose_pic)); % 分解后图像 title('decomposed pic');
figure(2);
colormap(map);
subplot(2,2,1);
image(abs(lt_pic)); % 左上方为低频分量--fi(x)*fi(y) title('/Phi(x)*/Phi(y)');
subplot(2,2,2);
image(abs(rt_pic)); % 矩阵右上为--fi(x)*psi(y) title('/Phi(x)*/Psi(y)');
subplot(2,2,3);
image(abs(lb_pic)); % 矩阵左下为--psi(x)*fi(y) title('/Psi(x)*/Phi(y)');
subplot(2,2,4);
image(abs(rb_pic)); % 右下方为高频分量--psi(x)*psi(y) title('/Psi(x)*/Psi(y)');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 5.重构源图像及结果显示 % construct_pic=decompose_matrix'*decompose_pic*decompose_matrix;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
l_re=l_zeros(end:-1:1); % 重构低通滤波 l_r=circshift(l_re',1)'; % 位置调整
h_re=h_zeros(end:-1:1); % 重构高通滤波
h_r=circshift(h_re',1)'; % 位置调整
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
top_pic=[lt_pic,rt_pic]; % 图像上半部分
t=0;
for i=1:T; % 行插值低频 if (mod(i,2)==0) topll(i,:)=top_pic(t,:); % 偶数行保持 else t=t+1; topll(i,:)=zeros(1,T); % 奇数行为零 end end;
for i=1:T; % 列变换
topcl_re(:,i)=ifft( fft(l_r).*fft(topll(:,i)') )'; % 圆周卷积<->FFT end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
bottom_pic=[lb_pic,rb_pic]; % 图像下半部分
t=0;
for i=1:T; % 行插值高频 if (mod(i,2)==0) bottomlh(i,:)=bottom_pic(t,:); % 偶数行保持 else bottomlh(i,:)=zeros(1,T); % 奇数行为零 t=t+1; end end;
for i=1:T; % 列变换
bottomch_re(:,i)=ifft( fft(h_r).*fft(bottomlh(:,i)') )'; % 圆周卷积<->FFT end;
construct1=bottomch_re+topcl_re; % 列变换重构完毕
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
left_pic=construct1(:,1:SUB_T); % 图像左半部分
t=0;
for i=1:T; % 列插值低频 if (mod(i,2)==0) leftll(:,i)=left_pic(:,t); % 偶数列保持 else t=t+1; leftll(:,i)=zeros(T,1); % 奇数列为零 end end;
for i=1:T; % 行变换
leftcl_re(i,:)=ifft( fft(l_r).*fft(leftll(i,:)) ); % 圆周卷积<->FFT end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
right_pic=construct1(:,SUB_T+1:T); % 图像右半部分 t=0; for i=1:T; % 列插值高频 if (mod(i,2)==0) rightlh(:,i)=right_pic(:,t); % 偶数列保持 else rightlh(:,i)=zeros(T,1); % 奇数列为零 t=t+1; end end;
for i=1:T; % 行变换
rightch_re(i,:)=ifft( fft(h_r).*fft(rightlh(i,:)) ); % 圆周卷积<->FFT end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% construct_pic=rightch_re+leftcl_re; % 重建全部图像
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 结果显示
figure(3); colormap(map);
subplot(2,1,1);
image(f); % 源图像显示 title('original pic'); subplot(2,1,2); image(abs(construct_pic)); % 重构源图像显示 title('reconstructed pic');
error=abs(construct_pic-f); % 重构图形与原始图像误值
figure(4);
mesh(error); % 误差三维图像 title('absolute error display'); |