MATLAB2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
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clear;clc;
T=256; % 图像维数
SUB_T=T/2; % 子图维数
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% 1.调原始图像矩阵
load wbarb; % 下载图像
f=X; % 原始图像
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% 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)
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% 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)');
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% 5.重构源图像及结果显示
% construct_pic=decompose_matrix'*decompose_pic*decompose_matrix;
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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
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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;
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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
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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(leftll(i,:)) ); % 圆周卷积<->FFT
end;
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right_pic=construct1(:,SUB_T+1:T); % 图像右半部分
t=0;
for i=1:T; % 列插值高频
if (mod(i,2)==0)
rightlh(:,i)=right_pic(:,t); % 偶数列保持
else
rightlh(:,i)=zeros(T,1); % 奇数列为零
t=t+1;
end
end;
for i=1:T; % 行变换
rightch_re(i,:)=ifft( fft(h_r).*fft(rightlh(i,:)) ); % 圆周卷积<->FFT
end;
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construct_pic=rightch_re+leftcl_re; % 重建全部图像
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% 结果显示
figure(3);
colormap(map);
subplot(2,1,1);
image(f); % 源图像显示
title('original pic');
subplot(2,1,2);
image(abs(construct_pic)); % 重构源图像显示
title('reconstructed pic');
error=abs(construct_pic-f); % 重构图形与原始图像误值
figure(4);
mesh(error); % 误差三维图像
title('absolute error display');
clear
clc
%在噪声环境下语音信号的增强
%语音信号为读入的声音文件
%噪声为正态随机噪声
sound=wavread('c12345.wav');
count1=length(sound);
noise=0.05*randn(1,count1);
for i=1:count1
signal(i)=sound(i);
end
for i=1:count1
y(i)=signal(i)+noise(i);
end
%在小波基'db3'下进行一维离散小波变换
[coefs1,coefs2]=dwt(y,'db3'); %[低频 高频]
count2=length(coefs1);
count3=length(coefs2);
energy1=sum((abs(coefs1)).^2);
energy2=sum((abs(coefs2)).^2);
energy3=energy1+energy2;
for i=1:count2
recoefs1(i)=coefs1(i)/energy3;
end
for i=1:count3
recoefs2(i)=coefs2(i)/energy3;
end
%低频系数进行语音信号清浊音的判别
zhen=160;
count4=fix(count2/zhen);
for i=1:count4
n=160*(i-1)+1:160+160*(i-1);
s=sound(n);
w=hamming(160);
sw=s.*w;
a=aryule(sw,10);
sw=filter(a,1,sw);
sw=sw/sum(sw);
r=xcorr(sw,'biased');
corr=max(r);
%为清音（unvoice）时，输出为1；为浊音（voice）时，输出为0
if corr>=0.8
output1(i)=0;
elseif corr<=0.1
output1(i)=1;
end
end
for i=1:count4
n=160*(i-1)+1:160+160*(i-1);
if output1(i)==1
switch abs(recoefs1(i))
case abs(recoefs1(i))<=0.002
recoefs1(i)=0;
case abs(recoefs1(i))>0.002 & abs(recoefs1(i))<=0.003
recoefs1(i)=sgn(recoefs1(i))*(0.003*abs(recoefs1(i))-0.000003)/0.002;
otherwise recoefs1(i)=recoefs1(i);
end
elseif output1(i)==0
recoefs1(i)=recoefs1(i);
end
end
%对高频系数进行语音信号清浊音的判别
count5=fix(count3/zhen);
for i=1:count5
n=160*(i-1)+1:160+160*(i-1);
s=sound(n);
w=hamming(160);
sw=s.*w;
a=aryule(sw,10);
sw=filter(a,1,sw);
sw=sw/sum(sw);
r=xcorr(sw,'biased');
corr=max(r);
%为清音（unvoice）时，输出为1；为浊音（voice）时，输出为0
if corr>=0.8
output2(i)=0;
elseif corr<=0.1
output2(i)=1;
end
end
for i=1:count5
n=160*(i-1)+1:160+160*(i-1);
if output2(i)==1
switch abs(recoefs2(i))
case abs(recoefs2(i))<=0.002
recoefs2(i)=0;
case abs(recoefs2(i))>0.002 & abs(recoefs2(i))<=0.003
recoefs2(i)=sgn(recoefs2(i))*(0.003*abs(recoefs2(i))-0.000003)/0.002;
otherwise recoefs2(i)=recoefs2(i);
end
elseif output2(i)==0
recoefs2(i)=recoefs2(i);
end
end
%在小波基'db3'下进行一维离散小波反变换
output3=idwt(recoefs1, recoefs2,'db3');
%对输出信号抽样点值进行归一化处理
maxdata=max(output3);
output4=output3/maxdata;
%读出带噪语音信号，存为'101.wav'
wavwrite(y,5500,16,'c101');
%读出处理后语音信号，存为'102.wav'
wavwrite(output4,5500,16,'c102');
function [I_W , S] = func_DWT(I, level, Lo_D, Hi_D);
%通过这个函数将I进行小波分解，并将分解后的一维向量转换为矩阵形式
% Matlab implementation of SPIHT (without Arithmatic coding stage)
% Wavelet decomposition
% input: I : input image
% level : wavelet decomposition level
% Lo_D : low-pass decomposition filter
% Hi_D : high-pass decomposition filter
% output: I_W : decomposed image vector
% S : corresponding bookkeeping matrix
% please refer wavedec2 function to see more
[C,S] = func_Mywavedec2(I,level,Lo_D,Hi_D);
S(:,3) = S(:,1).*S(:,2); % dim of detail coef nmatrices 求低频和每个尺度中高频的元素个数
%st=S(1,3)+S(2,3)*3+S(3,3)*3;%%%%对前两层加密
%C(1:st)=0;
L = length(S); %a求S的列数
I_W = zeros(S(L,1),S(L,2));%设一个与原图像大小相同的全零矩阵
% approx part
I_W( 1:S(1,1) , 1:S(1,2) ) = reshape(C(1:S(1,3)),S(1,1:2)); %将LL层从C中还原为S(1,1)*S(1,2)的矩阵
for k = 2 : L-1 %将C向量中还原出HL,HH,LH 矩阵
rows = [sum(S(1:k-1,1))+1:sum(S(1:k,1))];
columns = [sum(S(1:k-1,2))+1:sum(S(1:k,2))];
% horizontal part
c_start = S(1,3) + 3*sum(S(2:k-1,3)) + 1;
c_stop = S(1,3) + 3*sum(S(2:k-1,3)) + S(k,3);
I_W( 1:S(k,1) , columns ) = reshape( C(c_start:c_stop) , S(k,1:2) );
% vertical part
c_start = S(1,3) + 3*sum(S(2:k-1,3)) + S(k,3) + 1;
c_stop = S(1,3) + 3*sum(S(2:k-1,3)) + 2*S(k,3);
I_W( rows , 1:S(k,2) ) = reshape( C(c_start:c_stop) , S(k,1:2) );
% diagonal part
c_start = S(1,3) + 3*sum(S(2:k-1,3)) + 2*S(k,3) + 1;
c_stop = S(1,3) + 3*sum(S(2:k,3));
I_W( rows , columns ) = reshape( C(c_start:c_stop) , S(k,1:2) );
end
%%%%%%%mallat algorithm%%%%% clc; clear;tic; %%%%original signal%%%% f=100;%%frequence ts=1/800;%%抽样间隔 N=1:100;%%点数 s=sin(2*ts*pi*f.*N);%%源信号 figure(1) plot(s);%%%源信号s title('原信号'); grid on; %%%%小波滤波器%%%% ld=wfilters('db1','l');%%低通 hd=wfilters('db1','h');%%高通 figure(2) stem(ld,'r');%%%低通 grid on; figure(3) stem(hd,'b')%%%高通 grid on; %%%%% tem=conv(s,ld);%%低通和原信号卷积 ca1=dyaddown(tem);%%抽样 figure(4) plot(ca1); grid on; tem=conv(s,hd);%%高通和原信号卷积 cb1=dyaddown(tem);%%抽样 figure(5) plot(cb1); grid on; %%%%%%%% %[ca3,cb3]=dwt(s,'db1');%%小波变换 %%%%%%%% [lr,hr]=wfilters('db1','r');%%重构滤波器 figure(6) stem(lr); figure(7) stem(hr); tem=dyadup(cb1);%%插值 tem=conv(tem,hr);%%卷积 d1=wkeep(tem,100);%%去掉两头的分量 %%%%%%%%% tem=dyadup(ca1);%%插值 tem=conv(tem,lr);%%卷积 a1=wkeep(tem,100);%%去掉两头的分量 a=a1+d1;%%%重构原信号 %%%%%%%%% %a3=idwt(ca3,cb3,'db1',100);%%%小波逆变换 %%%%%%%%% figure(8) plot(a,'.b'); hold on; plot(s,'r'); grid on; title('重构信号和原信号的比较');toc; %figure(9) %plot(a3,'.b'); %hold on; %plot(s,'r'); %grid on; %title('重构信号和原信号的比较');
通用函数
Allnodes 计算树结点 appcoef 提取一维小波变换低频系数 appcoef2 提取二维小波分解低频系数 bestlevt 计算完整最佳小波包树 besttree 计算最佳(优)树 * biorfilt 双正交样条小波滤波器组 biorwavf 双正交样条小波滤波器 * centfrq 求小波中心频率 cgauwavf Complex Gaussian小波 cmorwavf coiflets小波滤波器 cwt 一维连续小波变换 dbaux Daubechies小波滤波器计算 dbwavf Daubechies小波滤波器 dbwavf(W) W='dbN' N=1,2,3,...,50 ddencmp 获取默认值阈值(软或硬)熵标准 depo2ind 将深度-位置结点形式转化成索引结点形式 detcoef 提取一维小波变换高频系数 detcoef2 提取二维小波分解高频系数 disp 显示文本或矩阵 drawtree 画小波包分解树(GUI) dtree 构造DTREE类 dwt 单尺度一维离散小波变换 dwt2 单尺度二维离散小波变换 dwtmode 离散小波变换拓展模式 * dyaddown 二元取样 * dyadup 二元插值 entrupd 更新小波包的熵值 fbspwavf B样条小波 gauswavf Gaussian小波 get 获取对象属性值 idwt 单尺度一维离散小波逆变换 idwt2 单尺度二维离散小波逆变换 ind2depo 将索引结点形式转化成深度—位置结点形式 * intwave 积分小波数 isnode 判断结点是否存在 istnode 判断结点是否是终结点并返回排列值 iswt 一维逆SWT(Stationary Wavelet Transform)变换 iswt2 二维逆SWT变换 leaves Determine terminal nodes mexihat 墨西哥帽小波 meyer Meyer小波 meyeraux Meyer小波辅助函数 morlet Morlet小波 nodease 计算上溯结点 nodedesc 计算下溯结点(子结点) nodejoin 重组结点 nodepar 寻找父结点 nodesplt 分割(分解)结点 noleaves Determine nonterminal nodes ntnode Number of terminal nodes ntree Constructor for the class NTREE * orthfilt 正交小波滤波器组 plot 绘制向量或矩阵的图形 * qmf 镜像二次滤波器 rbiowavf Reverse biorthogonal spline wavelet filters read 读取二进制数据 readtree 读取小波包分解树 * scal2frq Scale to frequency set shanwavf Shannon wavelets swt 一维SWT(Stationary Wavelet Transform)变换 swt2 二维SWT变换 symaux Symlet wavelet filter computation. symwavf Symlets小波滤波器 thselect 信号消噪的阈值选择 thodes References treedpth 求树的深度 treeord 求树结构的叉数 upcoef 一维小波分解系数的直接重构 upcoef2 二维小波分解系数的直接重构 upwlev 单尺度一维小波分解的重构 upwlev2 单尺度二维小波分解的重构 wavedec 单尺度一维小波分解 wavedec2 多尺度二维小波分解 wavedemo 小波工具箱函数demo * wavefun 小波函数和尺度函数 * wavefun2 二维小波函数和尺度函数 wavemenu 小波工具箱函数menu图形界面调用函数 * wavemngr 小波管理函数 waverec 多尺度一维小波重构 waverec2 多尺度二维小波重构 wbmpen Penalized threshold for wavelet 1-D or 2-D de-noising wcodemat 对矩阵进行量化编码 wdcbm Thresholds for wavelet 1-D using Birge-Massart strategy wdcbm2 Thresholds for wavelet 2-D using Birge-Massart strategy wden 用小波进行一维信号的消噪或压缩 wdencmp De-noising or compression using wavelets wentropy 计算小波包的熵 wextend Extend a vector or a matrix * wfilters 小波滤波器 wkeep 提取向量或矩阵中的一部分 * wmaxlev 计算小波分解的最大尺度 wnoise 产生含噪声的测试函数数据 wnoisest 估计一维小波的系数的标准偏差 wp2wtree 从小波包树中提取小波树 wpcoef 计算小波包系数 wpcutree 剪切小波包分解树 wpdec 一维小波包的分解 wpdec2 二维小波包的分解 wpdencmp 用小波包进行信号的消噪或压缩 wpfun 小波包函数 wpjoin 重组小波包 wprcoef 小波包分解系数的重构 wprec 一维小波包分解的重构 wprec2 二维小波包分解的重构 wpsplt 分割（分解）小波包 wpthcoef 进行小波包分解系数的阈值处理 wptree 显示小波包树结构 wpviewcf Plot the colored wavelet packet coefficients. wrcoef 对一维小波系数进行单支重构 wrcoef2 对二维小波系数进行单支重构 wrev 向量逆序 write 向缓冲区内存写进数据 wtbo Constructor for the class WTBO wthcoef 一维信号的小波系数阈值处理 wthcoef2 二维信号的小波系数阈值处理 wthresh 进行软阈值或硬阈值处理 wthrmngr 阈值设置管理 wtreemgr 管理树结构
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