Matlab小波工具箱入门

1、使用MATLAB小波工具箱进行小波分析:-兰-(algffn如J 7riOURE 7S AI嫌酬m)ikMlimcnionaL井 1hurik hx Ehbatida4« d' t Mt, H 1Cdiiinn<MM4(duni nsAir)时ft)丽1），如上图所示的小波分解过程，可以调用wfilters来获得指定小波的分解和综合滤波器系数，例如：% Set wavelet name.wname = 'db5'% Compute the four filters associated with wavelet name given% by the in

2、put string wname.Lo_D,Hi_D,Lo_R,Hi_R = wfilters(wname);subplot(221); stem(Lo_D);title('Decomposition low-pass filter');subplot(222); stem(Hi_D);title('Decomposition high-pass filter');subplot(223); stem(Lo_R);title('Reconstruction low-pass filter');subplot(224); stem(Hi_R);ti

3、tle('Reconstruction high-pass filter');xlabel('The four filters for db5')% Editing some graphical properties,% the following figure is generated.以上例子，得到db5'小波的分解和综合滤波器系数，并显示出来。下面是wfilters 的具体用法：wfiltersWavdet Skcrsnt>i(Lo_D, H i Dr Lo_R, Hi _R二 wfi Iters ( 1 urnaire1 'Fl,F

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8、e foHos hefsWnameM指定为列表中的任意一种小波，直接调用Lo_D,Hi_D,Lo_R,Hi_R = wfilters('wname')会返回分解和综合滤波器系数。如果只想返回其中的一些而不是全部，可以调用F1,F2 = wfilters('wname','type')其中type '可指定为4种类型，每种类型的具体意义详见matlab wfilters帮助。查看具体小波的信息waveinfo( 'wname )获得一个标准的正交变换/双正交变换的尺度和小波函数(数字近似值)PHI,PSI,XVAL = wavefu

9、n('wname',ITER)PHI1,PSI1,PHI2,PSI2,XVAL = wavefun('wname',ITER)例如% Set number of iterations and wavelet name.iter = 10;wav = 'sym4'% Compute approximations of the wavelet function using the% cascade algorithm.for i = 1:iterphi,psi,xval = wavefun(wav,i);plot(xval,psi);hold one

10、ndtitle( 'Approximations of the wavelet ' ,wav, .'for 1 to ',num2str(iter),' iterations');hold off如果已知小波分解滤波器系数，计算小波变换的最简单方法就是C,S = wavedec2(X,N,'wname')C,S = wavedec2(X,N,Lo_D,Hi_D)反过来，已知小波综合滤波器系数，计算反小波变换，只需X = waverec2(C,S,'wname')X = waverec2(C,S,Lo_R,Hi_R)

11、% 图片的小波分解clear allclcim = imread('././std_images/lena.bmp); % 灰度im = double(im);Lo_D,Hi_D = wfilters( 'haar','d');C,S= wavedec2(im,1,Lo_D,Hi_D);isize = prod(S(1,:);%cA = C(1:isize);cH = C(isize+(1:isize);cV = C(2*isize+(1:isize);cD = C(3*isize+(1:isize);%cA = reshape(cA,S(1,1),S(

12、1,2);cH = reshape(cH,S(2,1),S(2,2);cV = reshape(cV,S(2,1),S(2,2);cD = reshape(cD,S(2,1),S(2,2);%figure,colormap graysubplot(221),imagesc(cA);subplot(222),imagesc(cH);subplot(223),imagesc(cV);subplot(224),imagesc(cD);其中C是小波变换后的结果数据，以一维欠量的形式组织， S是二维数组，记录 了 C中数据的分布形式，详见 matlab的帮助文档。此外，dwtmode可以设定输 入的边界

13、处理方式。提取小波的系数。前面使用的wavedec2得到的C,S不是非常的直观，可以利用 小波工具箱中的函数appcoef2和detcoef2来机取近似矩阵和的n级的某一个 细节矩阵。A = appcoef2(C,S,'wname',N)A = appcoef2(C,S,'wname')D = detcoef2(O,C,S,N)针对特定的小波系数矩阵进行阈值化处理NC = wthcoef2('type',C,S,N,T,SORH)NC = wthcoef2('type',C,S,N)NC = wthcoef2('a'

14、;,C,S)NC = wthcoef2('t',C,S,N,T,SORH)使用wave2gray来显示小波分解的结果% 使用 wave2gray显示小波分解的结果，来自 dipum_1.1.4 toolboxclear allclcim = imread('././std_images/lena.bmp); % 灰度im = double(im);Lo_D,Hi_D = wfilters( 'haar','d');C,S= wavedec2(im,2,Lo_D,Hi_D);wave2gray(C,S);关丁 wave2gray更多用法详见

15、dipum_1.1.4 toolbox 的说明文档官方网站。小波综合(重建)：waverec2X = waverec2(C,S,'wname')X = waverec2(C,S,Lo_R,Hi_R)C,S是使用小波分解函数wavedec2得到的小波欠量和欠量描述矩阵，或者符合 这种规定形式的数据。返回X是实数图像矩阵，由丁计算误差，可能需要经过一 些处理才能正常显示。%小波综合clear allclcim = imread('././std_images/lena.bmp); % 灰度im = double(im);Lo_D,Hi_D = wfilters( 'haar','d');C,S= wavedec2(im,2,Lo_D,Hi_D);X = waverec2