Single-level discrete 2-D wavelet transform
dwt2 command performs a single-level two-dimensional wavelet decomposition with respect to either a particular wavelet ('
Hi_D) you specify.
[cA,cH,cV,cD] = dwt2(X,'
) computes the approximation coefficients matrix
cA and details coefficients matrices
cD (horizontal, vertical, and diagonal, respectively), obtained by wavelet decomposition of the input matrix
X. The '
wname' string contains the wavelet name.
[cA,cH,cV,cD] = dwt2(X,Lo_D,Hi_D) computes the two-dimensional wavelet decomposition as above, based on wavelet decomposition filters that you specify.
Hi_D must be the same length.
sx = size(X) and
lf = the length of filters; then
size(cA) = size(cH) = size(cV) = size(cD) = sa where
sa = ceil(sx/2),
sa = floor((sx+lf-1)/2).
For information about the different Discrete Wavelet Transform extension modes, see
[cA,cH,cV,cD] = dwt2(...,'
,MODE) computes the wavelet decomposition with the extension mode
MODE that you specify.
MODE is a string containing the desired extension mode.
An example of valid use is
% The current extension mode is zero-padding (see
dwtmode). % Load original image. load woman; % X contains the loaded image. % map contains the loaded colormap. nbcol = size(map,1); % Perform single-level decomposition % of X using db1. [cA1,cH1,cV1,cD1] = dwt2(X,'db1'); % Images coding. cod_X = wcodemat(X,nbcol); 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 ... ]; % Using some plotting commands, % the following figure is generated.
For images, there exist an algorithm similar to the one-dimensional case for two-dimensional wavelets and scaling functions obtained from one- dimensional ones by tensorial 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 steps for images:
To deal with signal-end effects involved by a convolution-based algorithm, a global variable managed by |
Daubechies, 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.)
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