matlab中wavedec2函数,[转载]小波滤波器–wavedec2函数

wavedec2函数:

1.功能:实现图像(即二维信号)的多层分解.多层,即多尺度.

2.格式:[c,s]=wavedec2(X,N,’wname’)

[c,s]=wavedec2(X,N,Lo_D,Hi_D)(我不讨论它)

3.参数说明:对图像X用wname小波基函数实现N层分解,

这里的小波基函数应该根据实际情况选择,具体办法可以：db1、db2、……db45、haar.

输出为c,s.c为各层分解系数,s为各层分解系数长度,也就是大小.

4.c的结构:c=[A(N)|H(N)|V(N)|D(N)|H(N-1)|V(N-1)|D(N-1)|H(N-2)|V(N-2)|D(N-2)|…|H(1)|V(1)|D(1)]

备注：c是一个行向量,size为:1*(size(X)),(e.g,X=256*256,then

c大小为:1*(256*256)=1*65536

A(N)代表第N层低频系数,

H(N)|V(N)|D(N)代表第N层高频系数,分别是水平,垂直,对角高频,

……

直至H(1)|V(1)|D(1).

5.s的结构:是储存各层分解系数长度

即第一行是A(N)的长度,

第二行是H(N)|V(N)|D(N)|的长度,

第三行是H(N-1)|V(N-1)|D(N-1)的长度,

……

倒数第二行是H(1)|V(1)|D(1)长度,

最后一行是X的长度(大小)

备注：size为(N+2)*2

wavedec2

Multilevel 2-D wavelet decomposition Syntax [C,S] =

wavedec2(X,N,’wname’)

[C,S] = wavedec2(X,N,Lo_D,Hi_D)

Description wavedec2 is a two-dimensional wavelet analysis

function.

[C,S] = wavedec2(X,N,’wname’) returns the wavelet decomposition

of the matrix X at level N, using the wavelet named in string

‘wname’ (see wfilters for more information).

Outputs are the decomposition vector C and the corresponding

bookkeeping matrix S. N must be a strictly positive integer (see

wmaxlev for more information).

Instead of giving the wavelet name, you can give the

filters.

For [C,S] = wavedec2(X,N,Lo_D,Hi_D), Lo_D is the decomposition

low-pass filter and Hi_D is the decomposition high-pass filter.

Vector C is organized as C = [ A(N) | H(N) | V(N) | D(N) | …

H(N-1) | V(N-1) | D(N-1) | … | H(1) | V(1) | D(1) ].

where A, H, V, D, are row vectors such that A = approximation

coefficients H = horizontal detail coefficients V = vertical detail

coefficients D = diagonal detail coefficients Each vector is the

vector column-wise storage of a matrix.

Matrix S is such that S(1,:) = size of approximation

coefficients(N) S(i,:) = size of detail coefficients(N-i+2) for i =

2, …N+1 and S(N+2,:) = size(X)

Examples

% The current extension mode is zero-padding (see dwtmode).

% Load original image.

load woman;

% X contains the loaded image.

% Perform decomposition at level 2

% of X using db1.

[c,s] = wavedec2(X,2,’db1′);

% Decomposition structure organization.

sizex = size(X)

sizex =

256

256

sizec = size(c)

sizec =

1

65536

val_s =

s

val_s =

64 64

64 64

128

128

256 256

Algorithm For images, an algorithm similar to the one-dimensional

case is possible for two-dimensional wavelets and scaling functions

obtained from one-dimensional ones by tensor product. This kind of

two-dimensional DWT leads to a decomposition of approximation

coefficients at level j in four components: the approximation at

level j+1, and the details in three orientations (horizontal,

vertical, and diagonal). The following chart describes the basic

decomposition step for images: So, for J=2, the two-dimensional

wavelet tree has the form See Alsodwt, waveinfo, waverec2,

wfilters, wmaxlev ReferencesDaubechies, I. (1992), Ten lectures on

wavelets, CBMS-NSF conference series in applied mathematics. SIAM

Ed. Mallat, S. (1989), “A theory for multiresolution signal

decomposition: the wavelet representation,” IEEE Pattern Anal. and

Machine Intell., vol. 11, no. 7, pp. 674-693. Meyer, Y. (1990),

Ondelettes et opérateurs, Tome 1, Hermann Ed. (English translation:

Wavelets and operators, Cambridge Univ. Press. 1993.

二维小波变换的函数

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函数名 函数功能

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dwt2 二维离散小波变换-单尺度

wavedec2 二维离散小波分解-多尺度 idwt2 二维离散小波反变换-单尺度

waverec2 二维信号的多层小波重构-多尺度

wrcoef2 由多层小波分解重构某一层的分解信号

upcoef2 由多层小波分解重构近似分量或细节分量

detcoef2 提取二维信号小波分解的细节分量

appcoef2 提取二维信号小波分解的近似分量 upwlev2 二维小波分解的单层重构

dwtpet2 二维周期小波变换

idwtper2 二维周期小波反变换

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