TRANSF/WAVE Image Wavelet [Algo] [Nbr_Scale] [Fc]
This command creates a file which contains the wavelet transform. The suffixe of a wavelet transform file is ``.wave''. It is automatically added to the name passed to the command. Several algorithms are proposed:
).
).
).
).
).
).
).
).
, the number of wavelet coefficients is
). Algorithms 4, 5, 6, and 7 are pyramidal (the number
of wavelet coefficients is 
), and the 8th algorithm
does not increase the number of data (the size of the wavelet
transform is 
). Due to the discretisation and the undersampling,
the properties of these algorithms are not the same. The 8th algorithm
is more compact, but is not isotropic (see section
). Algorithms 3, 6, and 7 compute the wavelet transform in
the Fourier space (see section ) and the undersampling
respect Shannon's theorem. Pyramidal algorithms 4 and 5 compute the
wavelet transform in the direct space, but need an interative
reconstruction. Algorithms 1 and 2 are isotropic but increase the number
of data. The 2D-discrete wavelet transform is not restricted the
previous algorithms. Other algorithms exist (see for example
Feauveau's one
[11] which is not diadic). The interest of the wavelet transform
is that it is a very flexible tool. We can adapt the transform to our
problem. We prefer the 8th for image compression, 6 and 7 for image
restoration, 2 for data analysis, etc.. The wavelet function can be
derived too from the specific problem to resolve (see [35]).
The parameter Nbr_Scale specifies the number of scales to compute.
The wavelet transform will contain 
wavelet
coefficients planes and one plane which will be the image at a very
low resolution.
The parameter Fc defines the cut-off frequency of the scaling
function (
). It is used only if the selected
wavelet transform algorithm
uses the FFT.