Wavelet Toolbox    

Single-level discrete 2-D wavelet transform



The dwt2 command performs a single-level two-dimensional wavelet decomposition with respect to either a particular wavelet ('wname', see wfilters for more information) or particular wavelet decomposition filters (Lo_D and Hi_D) you specify.

[cA,cH,cV,cD] = dwt2(X,'wname') computes the approximation coefficients matrix cA and details coefficients matrices cH, cV, and 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.

Lo_D and Hi_D must be the same length.

Let sx = size(X) and lf = the length of filters; then size(cA) = size(cH) = size(cV) = size(cD) = sa where sa = ceil(sx/2), if the DWT extension mode is set to periodization. For the other extension modes, sa = floor((sx+lf-1)/2).

For information about the different Discrete Wavelet Transform extension modes, see dwtmode.

[cA,cH,cV,cD] = dwt2(...,'mode',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



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:

See Also
dwtmode, idwt2, wavedec2, waveinfo


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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