維小波變換MATLAB實(shí)現(xiàn)

1、二維小波變換matlab實(shí)現(xiàn) dwt2函數(shù) 功能：二維離散小波變換 格式：ca,ch,cv,cd=dwt2(x,wname) ca,ch,cv,cd=dwt2(x,lo_d,hi_d) 說明：ca,ch,cv,cd=dwt2(x,wname)使用指定的小波基函數(shù)wname對(duì)二維信號(hào)x進(jìn)行二維離散小波變幻；ca，ch,cv,cd分別為近似分量、水平細(xì)節(jié)分量、垂直細(xì)節(jié)分量和對(duì)角細(xì)節(jié)分量；ca,ch,cv,cd=dwt2(x,lo_d,hi_d)使用指定的分解低通和高通濾波器lo_d和hi_d分解信號(hào)x。 load woman; nbcol = size(map,1);%返回矩陣的行數(shù)和列數(shù) ca1

2、,ch1,cv1,cd1 = dwt2(x,db1); cod_x=wcodemat(x,nbcol);%返回矩陣x的編碼矩陣，nbcol為編碼的最大值 cod_ca1=wcodemat(ca1,nbcol); cod_ch1=wcodemat(ch1,nbcol); cod_cv1=wcodemat(cv1,nbcol); cod_cd1=wcodemat(cd1,nbcol); dec2d=cod_ca1,cod_ch1;cod_cv1,cod_cd1; subplot(1,2,1),imshow(cod_x,); title(量化后的圖像); subplot(1,2,2),imshow(

3、dec2d,); title(二維離散小波分解后的圖像); idwt2函數(shù) 功能：二維離散小波反變換 格式：x=idwt2(ca,ch,cv,cd,wname) x=idwt2(ca,ch,cv,cd,lo_r,hi_r) x=idwt2(ca,ch,cv,cd,wname,s) x=idwt2(ca,ch,cv,cd,lo_r,hi_r,s) 說明：x=idwt2(ca,ch,cv,cd,wname)由信號(hào)小波分解的近似信號(hào)ca和細(xì)節(jié)信號(hào)ch、ch、cv、cd經(jīng)小波反變換重構(gòu)原信號(hào)x；x=idwt2(ca,ch,cv,cd,lo_r,hi_r)使用指定的重構(gòu)低通和高通濾波器lo_r和hi_r

4、重構(gòu)原信號(hào)x；x=idwt2(ca,ch,cv,cd,wname,s)和x=idwt2(ca,ch,cv,cd,lo_r,hi_r,s)返回中心附近的s個(gè)數(shù)據(jù)點(diǎn)。 load woman; sx=size(x); ca1,ch1,cv1,cd1=dwt2(x,db4); a0=idwt2(ca1,ch1,cv1,cd1,db4,sx); subplot(1,2,1),imshow(x,) title(原始圖像); subplot(1,2,2),imshow(a0,) title(由二維小波分解重構(gòu)后的圖像); wavedec2函數(shù) 功能：二維信號(hào)的多層小波分解 格式：c,s=wavedec2(x

5、,n,wname) c,s=wavedec2(x,n,lo_d,hi_d) 說明：c,s=wavedec2(x,n,wname)用小波基函數(shù)wname對(duì)二維信號(hào)x進(jìn)行n層分解；c,s=wavedec2(x,n,lo_d,hi_d)用指定的分解低通和高通濾波器lo_d和hi_d分解信號(hào)x。 waverec2函數(shù) 說明：二維信號(hào)的多層小波重構(gòu) 格式：x=waverec2(c,s,wname) x=waverec2(c,s,lo_r,hi_r) 說明：x=waverec2(c,s,wname)由多層二維小波分解的結(jié)果c、s重構(gòu)原始信號(hào)x，wname為使用的小波基函數(shù)；x=waverec2(c,s,l

6、o_r,hi_r)使用重構(gòu)低通和高通濾波器lo_r和hi_r重構(gòu)原信號(hào)。 load woman; c,s=wavedec2(x,2,sym4); a0=waverec2(c,s,sym4); subplot(1,2,1),imshow(x,) title(原始圖像); subplot(1,2,2),imshow(a0,) title(重構(gòu)后的圖像);appcoef2提取二維信號(hào)小波分解的近似分量 load woman; c,s=wavedec2(x,3,db1);%用db1小波進(jìn)行三層分解 ca1=appcoef2(c,s,db1,1);%提取一層近似分量 ca2=appcoef2(c,s,d

7、b2,2);%提取二層近似分量 imshow(x,); title(原始圖像); figure,imshow(ca1,) title (第一層近似分量); figure,imshow(ca2,) title(第二層近似分量);detcoef2提取二維信號(hào)小波分解的細(xì)節(jié)分量load woman;c,s=wavedec2(x,3,db1);chd2=detcoef2(h,c,s,1);cvd2=detcoef2(v,c,s,1);cdd2=detcoef2(d,c,s,1);imshow(x,)title(原始圖像);figuresubplot(1,3,1),imshow(chd2,)title(

8、第一層分解的水平細(xì)節(jié));subplot(1,3,2),imshow(cvd2,)title(第一層分解的垂直細(xì)節(jié));subplot(1,3,3),imshow(cdd2,)title(第一層分解的對(duì)角細(xì)節(jié));wrcoef2由多層小波分解重構(gòu)某一層的分解信號(hào) clear allload wbarb;image(x);colormap(map);colorbar;i=ind2gray(x,map);figure;i=imadjust(i,stretchlim(i),0,1);imshow(i);%j=imadjust(i,low_in;high_in,low_out,high_out) 將 i 中

9、的亮度值映射到 j 中的新值wname=sym2;c,s=wavedec2(i,2,wname);ca1=appcoef2(c,s,wname,1);ch1,cv1,cd1=detcoef2(all,c,s,1);ca2=appcoef2(c,s,wname,2);ch2,cv2,cd2=detcoef2(all,c,s,2);a1=wrcoef2(a,c,s,wname,1);h1=wrcoef2(h,c,s,wname,1);v1=wrcoef2(v,c,s,wname,1);d1=wrcoef2(d,c,s,wname,1);a2=wrcoef2(a,c,s,wname,2);h2=wr

10、coef2(h,c,s,wname,2);v2=wrcoef2(v,c,s,wname,2);d2=wrcoef2(d,c,s,wname,2);figure;subplot(2,2,1);a1=abs(a1);a1=imadjust(a1,stretchlim(a1),0,1);imshow(a1);title(approximation a1)subplot(2,2,2);h1=abs(h1);h1=imadjust(h1,stretchlim(h1),0,1);imshow(h1);title(horizontal detail h1)subplot(2,2,3);v1=abs(v1);

11、v1=imadjust(v1,stretchlim(v1),0,1);imshow(v1);title(vertical detail v1)subplot(2,2,4);d1=abs(d1);d1=imadjust(d1,stretchlim(d1),0,1);imshow(d1);title(diagonal detail d1)figure;subplot(2,2,1);a2=abs(a2);a2=imadjust(a2,stretchlim(a2),0,1);imshow(a2);title(approximation a2)subplot(2,2,2);h2=abs(h2);h2=i

12、madjust(h2,stretchlim(h2),0,1);imshow(h2);title(horizontal detail h2)subplot(2,2,3);v2=abs(v2);v2=imadjust(v2,stretchlim(v2),0,1);imshow(v2);title(vertical detail v2)subplot(2,2,4);d2=abs(d2);d2=imadjust(d2,stretchlim(d2),0,1);imshow(d2);title(diagonal detail d2)upcoef2由多層小波分解重構(gòu)近似分量或細(xì)節(jié)分量 load woman;c,s=wavedec2(x,2,db4);siz=s(size(s,1),:);cal=appcoef2(c,s,db4,1);a1=upcoef2(a,cal,db4,1,siz);chd1=detcoef2(h,c,s,1);hd1=upcoef2(h,chd1,db4,1,siz);cvd1=detcoef2(v,c,s,1);vd1=upcoef2(h,cvd1,db4,1,siz);cdd1=detcoef2(d,c,s,1