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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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