在MATLAB环境下，实现对小波变换信号处理的有关试验.zip

load noiswom; %装载图像信号 whos [swa,swh,swv,swd] = swt2(X,1,'db1'); %完成图像的单层次小波分解 whos %观察各个系数向量的结构 figure(1); map = pink(size(map,1)); %显示低频和高频系数 colormap(map) subplot(2,2,1), image(wcodemat(swa,192)); title('Approximation swa') subplot(2,2,2), image(wcodemat(swh,192)); title('Horiz. Detail swh') subplot(2,2,3), image(wcodemat(swv,192)); title('Vertical Detail swv') subplot(2,2,4), image(wcodemat(swd,192)); title('Diag. Detail swd') A0 = iswt2(swa,swh,swv,swd,'db1'); %通过平稳小波逆变换重构图像 err = max(max(abs(X-A0))) %检查重构误差 nulcfs = zeros(size(swa)); %从第三步中产生的系数swa、swh、swv和swd构造第一层的低频和高频（A1、H1、V1和D1）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'); figure(2); %显示第一层的分解结果 colormap(map) subplot(2,2,1), image(wcodemat(A1,192)); title('Approximation A1') subplot(2,2,2), image(wcodemat(H1,192)); title('Horiz. Detail H1') subplot(2,2,3), image(wcodemat(V1,192)); title('Vertical Detail V1') subplot(2,2,4), image(wcodemat(D1,192)); title('Diag. Detail D1') [swa,swh,swv,swd] = swt2(X,3,'db1'); %采用db1来完成多尺度二维离散平稳小波分解 clear A0 A1 D1 H1 V1 err nulcfs %观察swa,swh,swv,swd的存储结构 whos figure(3); %显示多尺度二维平稳小波分解结果 colormap(map) kp = 0; for i = 1:3 subplot(3,4,kp+1), image(wcodemat(swa(:,:,i),192)); title(['Approx. cfs level ',num2str(i)]) subplot(3,4,kp+2), image(wcodemat(swh(:,:,i),192)); title(['Horiz. Det. cfs level ',num2str(i)]) subplot(3,4,kp+3), image(wcodemat(swv(:,:,i),192)); title(['Vert. Det. cfs level ',num2str(i)]) subplot(3,4,kp+4), image(wcodemat(swd(:,:,i),192)); title(['Diag. Det. cfs level ',num2str(i)]) kp = kp + 4; end mzero = zeros(size(swd)); %从系数中重构第3层的低频信号 A = mzero; A(:,:,3) = iswt2(swa,mzero,mzero,mzero,'db1'); H = mzero; V = mzero; %重构第1、2、3层的高频信号 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 A(:,:,2) = A(:,:,3) + H(:,:,3) + V(:,:,3) + D(:,:,3); %通过第3层的低频部分和第1、2、3层的高频部分重构第1、2层的低频部分 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),192)); title(['Approx. level ',num2str(i)]) subplot(3,4,kp+2), image(wcodemat(H(:,:,i),192)); title(['Horiz. Det. level ',num2str(i)]) subplot(3,4,kp+3), image(wcodemat(V(:,:,i),192)); title(['Vert. Det. level ',num2str(i)]) subplot(3,4,kp+4), image(wcodemat(D(:,:,i),192)); title(['Diag. Det. level ',num2str(i)]) kp = kp + 4; end; thr = 44.5; %阈值消噪 sorh = 's'; dswh = wthresh(swh,sorh,thr); dswv = wthresh(swv,sorh,thr); dswd = wthresh(swd,sorh,thr); clean = iswt2(swa,dswh,dswv,dswd,'db1'); thr = 44.5; sorh = 's'; dswh = wthresh(swh,sorh,thr); dswv = wthresh(swv,sorh,thr); dswd = wthresh(swd,sorh,thr); clean = iswt2(swa,dswh,dswv,dswd,'db1'); figure(5); %对比消噪前后的图像 colormap(map) subplot(1,2,1), image(wcodemat(X,192)); title('Original image') subplot(1,2,2), image(wcodemat(clean,192)); title('De-noised image')