小波分析理论与Matlab 7实现

% 装载图像信号 load belmont2; % 完成图像的单层次小波分解 [swa,swh,swv,swd] = swt2(X,1,'db1'); % 显示低频和高频系数 map = pink(size(map,1)); figure(1) colormap(map) nbcol = size(map,1) subplot(2,2,1), image(wcodemat(swa,nbcol)); title('低频系数swa') subplot(2,2,2), image(wcodemat(swh,nbcol)); title('水平方向高频系数swh') subplot(2,2,3), image(wcodemat(swv,nbcol)); title('垂直方向高频系数swv') subplot(2,2,4), image(wcodemat(swd,nbcol)); title('对角方向高频系数swd') % 通过平稳小波逆变换重构图像 A0 = iswt2(swa,swh,swv,swd,'db1'); nulcfs = zeros(size(swa)); % 由分解系数重构第一层的低频和高频部分 A1 = iswt2(swa,nulcfs,nulcfs,nulcfs,'db1'); H1 = iswt2(nulcfs,swh,nulcfs,nulcfs,'db1'); V1 = iswt2(nulcfs,nulcfs,swv,nulcfs,'db1'); D1 = iswt2(nulcfs,nulcfs,nulcfs,swd,'db1'); % 显示第一层的分解结果，包括显示低频和高频部分 figure(2) colormap(map) subplot(2,2,1), image(wcodemat(A1,nbcol)); title('低频 A1') subplot(2,2,2), image(wcodemat(H1,nbcol)); title('水平高频H1') subplot(2,2,3), image(wcodemat(V1,nbcol)); title('垂直高频V1') subplot(2,2,4), image(wcodemat(D1,nbcol)); title('对角高频D1') % 图像的多层二维离散平稳小波分解 [swa,swh,swv,swd] = swt2(X,3,'db1'); % 显示多层二维离散平稳小波分解结果 figure(3) colormap(map) kp = 0; for i = 1:3 subplot(3,4,kp+1), image(wcodemat(swa(:,:,i),nbcol)); title(['低频系数：level ',num2str(i)]) subplot(3,4,kp+2), image(wcodemat(swh(:,:,i),nbcol)); title(['水平高频系数：level ',num2str(i)]) subplot(3,4,kp+3), image(wcodemat(swv(:,:,i),nbcol)); title(['垂直高频系数：level ',num2str(i)]) subplot(3,4,kp+4), image(wcodemat(swd(:,:,i),nbcol)); title(['对角高频系数：level ',num2str(i)]) kp = kp + 4; end % 从系数中重构第3层的低频信号 mzero = zeros(size(swd)); A = mzero; A(:,:,3) = iswt2(swa,mzero,mzero,mzero,'db1'); % 由系数重构第1、2、3层的高频信号 H = mzero; V = mzero; D = mzero; for i = 1:3 swcfs = mzero; swcfs(:,:,i) = swh(:,:,i); H(:,:,i) = iswt2(mzero,swcfs,mzero,mzero,'db1'); swcfs = mzero; swcfs(:,:,i) = swv(:,:,i); V(:,:,i) = iswt2(mzero,mzero,swcfs,mzero,'db1'); swcfs = mzero; swcfs(:,:,i) = swd(:,:,i); D(:,:,i) = iswt2(mzero,mzero,mzero,swcfs,'db1'); end % 重构第1、2层的低频部分 A(:,:,2) = A(:,:,3) + H(:,:,3) + V(:,:,3) + D(:,:,3); A(:,:,1) = A(:,:,2) + H(:,:,2) + V(:,:,2) + D(:,:,2); figure(4) % 显示第1、2、3层的低频和高频部分 colormap(map) kp = 0; for i = 1:3 subplot(3,4,kp+1), image(wcodemat(A(:,:,i),nbcol)); title(['低频：level ',num2str(i)]) subplot(3,4,kp+2), image(wcodemat(H(:,:,i),nbcol)); title(['水平高频：level ',num2str(i)]) subplot(3,4,kp+3), image(wcodemat(V(:,:,i),nbcol)); title(['垂直高频：level ',num2str(i)]) subplot(3,4,kp+4), image(wcodemat(D(:,:,i),nbcol)); title(['对角高频：level ',num2str(i)]) kp = kp + 4; end