gives the lifting wavelet transform (LWT) of an array of data.
gives the lifting wavelet transform using the wavelet wave.
gives the lifting wavelet transform using r levels of refinement.
Details and Options
- LiftingWaveletTransform gives a DiscreteWaveletData object.
- Properties of the DiscreteWaveletData dwd can be found using dwd["prop"], and a list of available properties can be found using dwd["Properties"].
- The resulting wavelet coefficients are arrays of the same depth as the input data.
- The data can be any of the following:
list arbitrary-rank numerical array image arbitrary Image object audio an Audio or sampled Sound object
- The possible wavelets wave include:
BiorthogonalSplineWavelet[…] B-spline-based wavelet CDFWavelet[…] Cohen-Daubechies-Feauveau 9/7 wavelet CoifletWavelet[…] symmetric variant of Daubechies wavelets DaubechiesWavelet[…] the Daubechies wavelets HaarWavelet[…] classic Haar wavelet ReverseBiorthogonalSplineWavelet[…] B-spline-based wavelet (reverse dual and primal) SymletWavelet[…] least asymmetric orthogonal wavelet
- The default wave is HaarWavelet.
- With higher settings for the refinement level r, larger scale features are resolved.
- With refinement level r, LiftingWaveletTransform internally pre-pads data so that each dimension is a multiple of . The padding values used for pre-padding are given by the setting of the Padding option. »
- With refinement level Full, r is given by .
- The default levels of refinement r are given by , where is the integer factorization of the length of data. For multi-dimensional data, the same computation is done for each dimension and the resulting minimum refinement level is used. »
- The tree of wavelet coefficients at level consists of coarse coefficients and detail coefficients , with representing the input data.
- The dimensions of and are given by , where is given by , where is the input data dimension. »
- The following options can be given:
Method Automatic method to use Padding "Periodic" how to extend data beyond boundaries WorkingPrecision MachinePrecision precision to use in internal computations
- The settings for Padding include "Periodic" for periodic repetition of the dataset in each dimension and for constant padding.
- With the setting Method->"IntegerLifting", integer data will transform to integer coefficients, in which case input image data of type "Real" is converted to type "Byte".
- InverseWaveletTransform gives the inverse transform.
Examplesopen allclose all
Basic Examples (3)
Compute a lifting wavelet transform using the HaarWavelet:
Use Normal to view all coefficients:
Transform an Image object: