二维小波变换MATLAB实现

1、二维小波变换MATLAB实现 dwt2函数 功能：二维离散小波变换 格式：cA,cH,cV,cD=dwt2(X,wname) cA,cH,cV,cD=dwt2(X,Lo_D,Hi_D) 说明：cA,cH,cV,cD=dwt2(X,wname)使用指定的小波基函数wname对二维信号X进行二维离散小波变幻；cA，cH,cV,cD分别为近似分量、水平细节分量、垂直细节分量和对角细节分量；cA,cH,cV,cD=dwt2(X,Lo_D,Hi_D)使用指定的分解低通和高通滤波器Lo_D和Hi_D分解信号X。 load woman; nbcol = size(map,1);%返回矩阵的行数和列数 cA1

2、,cH1,cV1,cD1 = dwt2(X,db1); cod_x=wcodemat(X,nbcol);%返回矩阵X的编码矩阵，nbcol为编码的最大值 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(量化后的图像); subplot(1,2,2),imshow(

3、dec2d,); title(二维离散小波分解后的图像); idwt2函数 功能：二维离散小波反变换 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) 说明：X=idwt2(cA,cH,cV,cD,wname)由信号小波分解的近似信号cA和细节信号cH、cH、cV、cD经小波反变换重构原信号X；X=idwt2(cA,cH,cV,cD,Lo_R,Hi_R)使用指定的重构低通和高通滤波器Lo_R和Hi_R

4、重构原信号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个数据点。 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(原始图像); subplot(1,2,2),imshow(A0,) title(由二维小波分解重构后的图像); wavedec2函数 功能：二维信号的多层小波分解 格式：C,S=wavedec2(X

5、,N,wname) C,S=wavedec2(X,N,Lo_D,Hi_D) 说明：C,S=wavedec2(X,N,wname)用小波基函数wname对二维信号X进行N层分解；C,S=wavedec2(X,N,Lo_D,Hi_D)用指定的分解低通和高通滤波器Lo_D和Hi_D分解信号X。 waverec2函数 说明：二维信号的多层小波重构 格式：X=waverec2(C,S,wname) X=waverec2(C,S,Lo_R,Hi_R) 说明：X=waverec2(C,S,wname)由多层二维小波分解的结果C、S重构原始信号X，wname为使用的小波基函数；X=waverec2(C,S,L

6、o_R,Hi_R)使用重构低通和高通滤波器Lo_R和Hi_R重构原信号。 load woman; c,s=wavedec2(X,2,sym4); a0=waverec2(c,s,sym4); subplot(1,2,1),imshow(X,) title(原始图像); subplot(1,2,2),imshow(a0,) title(重构后的图像);appcoef2提取二维信号小波分解的近似分量 load woman; c,s=wavedec2(X,3,db1);%用db1小波进行三层分解 ca1=appcoef2(c,s,db1,1);%提取一层近似分量 ca2=appcoef2(c,s,d

7、b2,2);%提取二层近似分量 imshow(X,); title(原始图像); figure,imshow(ca1,) title (第一层近似分量); figure,imshow(ca2,) title(第二层近似分量);detcoef2提取二维信号小波分解的细节分量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(原始图像);figuresubplot(1,3,1),imshow(chd2,)title(

8、第一层分解的水平细节);subplot(1,3,2),imshow(cvd2,)title(第一层分解的垂直细节);subplot(1,3,3),imshow(cdd2,)title(第一层分解的对角细节);wrcoef2由多层小波分解重构某一层的分解信号 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) 将 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由多层小波分解重构近似分量或细节分量 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