115454545.rar_115454545.rar_小波

2代小波示意程序 2维小波变换经典程序 Daubechies小波基的构造 采用多孔trous算法(undecimated wavelet transform)实现小波变换 平移变换平移法(cycle_spinning)消除gibbs效应 提升法97经典程序 消失矩作用的程序 小波插值与小波构造 小波滤波器构造和消噪程序 小波谱分析mallat算法经典程序 2代小波示意程序 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 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%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% 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); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% 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); 2维小波变换经典程序 % 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(le