小波變換的圖像處理%MATLAB2維小波變換經典程序 % FWT_DB.M; % 此示意程序用DWT實現二維小波變換 % 編程時間2004-4-10，編程人沙威 %%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%% clear; clc; T=256; % 圖像維數 SUB_T=T/2; % 子圖維數 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1.調原始圖像矩陣 load wbarb; % 下載圖像 f=X; % 原始圖像 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 2.進行二維小波分解 l=wfilters('db10','l'); % db10（消失矩為10)低通分解濾波器沖擊響應（長度為20） L=T-length(l); l_zeros=[l,zeros(1,L)]; % 矩陣行數與輸入圖像一致，為2的整數冪 h=wfilters('db10','h'); % db10（消失矩為10)高通分解濾波器沖擊響應（長度為20） h_zeros=[h,zeros(1,L)]; % 矩陣行數與輸入圖像一致，為2的整數冪 for i=1:T; % 列變換 row(1:SUB_T,i)=dyaddown( ifft( fft(l_zeros).*fft(f(:,i)') ) ).'; % 圓周卷積FFT row(SUB_T+1:T,i)=dyaddown( ifft( fft(h_zeros).*fft(f(:,i)') ) ).'; % 圓周卷積FFT end; for j=1:T; % 行變換 line(j,1:SUB_T)=dyaddown( ifft( fft(l_zeros).*fft(row(j,:)) ) ); % 圓周卷積FFT line(j,SUB_T+1:T)=dyaddown( ifft( fft(h_zeros).*fft(row(j,:)) ) ); % 圓周卷積FFT end; decompose_pic=line; % 分解矩陣 % 圖像分為四塊 lt_pic=decompose_pic(1:SUB_T,1:SUB_T); % 在矩陣左上方為低頻分量--fi(x)*fi(y) rt_pic=decompose_pic(1:SUB_T,SUB_T+1:T); % 矩陣右上為--fi(x)*psi(y) lb_pic=decompose_pic(SUB_T+1:T,1:SUB_T); % 矩陣左下為--psi(x)*fi(y) rb_pic=decompose_pic(SUB_T+1:T,SUB_T+1:T); % 右下方為高頻分量--psi(x)*psi(y) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 3.分解結果顯示 figure(1); colormap(map); subplot(2,1,1); image(f); % 原始圖像 title('original pic'); subplot(2,1,2); image(abs(decompose_pic)); % 分解后圖像 title('decomposed pic'); figure(2); colormap(map); subplot(2,2,1); image(abs(lt_pic)); % 左上方為低頻分量--fi(x)*fi(y) title('\Phi(x)*\Phi(y)'); subplot(2,2,2); image(abs(rt_pic)); % 矩陣右上為--fi(x)*psi(y) title('\Phi(x)*\Psi(y)'); subplot(2,2,3); image(abs(lb_pic)); % 矩陣左下為--psi(x)*fi(y) title('\Psi(x)*\Phi(y)'); subplot(2,2,4); image(abs(rb_pic)); % 右下方為高頻分量--psi(x)*psi(y) title('\Psi(x)*\Psi(y)'); %%%%%%%