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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:
- 1.
- à trous algorithm with a linear scaling function.
The wavelet function is the difference between two resolutions
(see 14.4.3).
- 2.
- à trous with a B3-spline scaling function (default value).
The wavelet function is the difference between two resolutions
(see 14.4.3).
- 3.
- algorithm using the Fourier transform, without any reduction
of the samples between two scales. The Fourier transform of the scaling
function is a b3-spline and the wavelet function is the
difference between two resolutions (14.4.5).
- 4.
- pyramidal algorithm in the direct space, with a linear scaling
function (see section 14.4.4).
- 5.
- pyramidal algorithm in the direct space, with a b3-spline
scaling function (see section 14.4.4).
- 6.
- algorithm using the Fourier transform with a reduction of
the samples between two scales. The Fourier transform of the scaling
function is a b3-spline the wavelet function is the difference
between two resolutions (14.4.5).
- 7.
- algorithm using the Fourier transform with a reduction of the
samples between two scales. The Fourier transform of the scaling
function is a b3-spline. The wavelet function is the difference
between the square of two resolutions (14.4.5).
- 8.
- Mallat's Algorithm with biorthogonal filters (14.4.2).
The parameter Algo can be chosen between 1 and 8. If Algo is in
{1,2,3}, the number of data of the wavelet transform is equal to
the number of pixels multiplied by the number of scales (if the number
of pixels of the image is N2, 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 N2). 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
14.4.2). Algorithms 3, 6, and 7 compute the wavelet transform in
the Fourier space (see section 14.4.5) 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.
Next: RECONS/WAVE
Up: Commands Description
Previous: Commands Description
Petra Nass
1999-06-15