博客

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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’);

（这一段比较纠结，有时间研究下）

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