小波实验报告双树复小波变换.doc

一、题目：双树复小波变换
二、目的：双树复小波和实小波变换的比较
三、算法及其实现：提取阶梯型边界点
算法。

幅值:
相位：

代码实现。
我采用Matlab函数编程实现。具体程序见shift_test_2D.m，drawcirc.m，setfig.m，dtwavexfm2.m，dtwaveifm2.m,waveifm2.m,wavexfm2.m
SkelMap.m。
设和分别是双正交对偶尺度函数与对偶小波，，，和是相应的低通滤波器和高通滤波器，即它们满足
实部：虚部：

双树复小波变换可以通过离散小波变换DWT实现：一个DWT产生实部，另一个产生虚部。

实现工具：Matlab
程序代码：
（1）shift_test_2D.m：
%shift_test_2D.m
%
%M-filetoperforma4-levelwavelettransformonacircleusingQ-shift
%dualwavelettreeandDWT,andtocompareshiftinvarianceproperties.
%
%NickKingsbury,CambridgeUniversity,May2002.

clearall
closeall

%Drawacirculardisc.
x=round((drawcirc(64,1,0,0,256)-0.5)*200);
setfig(1);
colormap(gray(256))
image(min(max(x+128,1),256));
set(gca,'position',[0.10.25.25.5]);
axis('off');
axis('image');

%draw(xx);
title('Input(256x256)','FontSize',14);drawnow

%Do4levelsofCWT.
[Yl,Yh]=dtwavexfm2(x,4,'near_sym_b','qshift_b');

%Looptoreconstructoutputfromcoefsateachlevelinturn.
%Startswiththefinestlevel.
titl=['1st';'2nd';'3rd';'4th';'Low'];

yy=zeros(size(x).*[23]);
yt1=1:size(x,1);yt2=1:size(x,2);

formlev=1:5,
mask=zeros(6,5);
mask(:,mlev)=1;
z=dtwaveifm2(Yl*mask(1,5),Yh,'near_sym_b','qshift_b',mask);
figure;draw(z);drawnow

yy(yt1,yt2)=z;
yt2=yt2+size(x,2)/2;
end

%disp('Pressakey...')
%pause

%NowdosamewithDWT.

%Do4levelsofRealDWTusing'antonini'(9,7)-tapfilters.
[Yl,Yh]=wavexfm2(x,4,'antonini');

yt1=[1:size(x,1)]+size(x,1);yt2=1:size(x,2);

formlev=1:5,
mask=zeros(3,5);
mask(:,mlev)=1;
z=waveifm2(Yl*mask(1,5),Yh,'antonini',mask);
figure;draw(z);drawnow

yy(yt1,yt2)=z;
yt2=yt2+size(x,2)/2;
end

figure;
setfig(gcf);
colormap(gray(256))
image(min(max(yy+128,1),256));
set(gca,'position',[0.10.1.8.8]);
axis('off');
axis('image');
holdon
plot(128*[[1;1]*[1:4][0;6]]+1,128*[[0;4]*[1111][2;2]]+1,'-k');
holdoff

title('Componentsofreconstructed''disc''images','FontSize',14);
text(-0.01*size(yy,2),0.25*size(yy,1),'DTCWT','horiz','r');
text(0.02*size(yy,2),1.02*size(yy,1),'wavelets:','horiz','r','vert','t');
text(-0.01*size(yy,2),0.75*size(yy,1),'DWT','hori