StationaryWaveletTransform

StationaryWaveletTransform[data]
gives the stationary wavelet transform (SWT) of an array of data.

StationaryWaveletTransform[data,wave]
gives the stationary wavelet transform using the wavelet wave.

StationaryWaveletTransform[data,wave,r]
gives the stationary wavelet transform using r levels of refinement.

StationaryWaveletTransform[image,]
gives the stationary wavelet transform of an image.

StationaryWaveletTransform[sound,]
gives the stationary wavelet transform of sampled sound.

Details and OptionsDetails and Options

  • StationaryWaveletTransform 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"].
  • StationaryWaveletTransform is similar to DiscreteWaveletTransform except that no subsampling occurs at any refinement level and the resulting coefficient arrays all have the same dimensions as the original data.
  • The data can be a rectangular array of any depth.
  • By default, input image is converted to an image of type .
  • The resulting wavelet coefficients are arrays of the same depth and dimensions as the input data.
  • The possible wavelets wave include:
  • BattleLemarieWavelet[]BattleLemarié wavelets based on B-spline
    BiorthogonalSplineWavelet[]B-spline-based wavelet
    CoifletWavelet[]symmetric variant of Daubechies wavelets
    DaubechiesWavelet[]the Daubechies wavelets
    HaarWavelet[]classic Haar wavelet
    MeyerWavelet[]wavelet defined in the frequency domain
    ReverseBiorthogonalSplineWavelet[]B-spline-based wavelet (reverse dual and primal)
    ShannonWavelet[]sinc function-based wavelet
    SymletWavelet[]least asymmetric orthogonal wavelet
  • The default wave is HaarWavelet[].
  • With higher settings for the refinement level r, larger-scale features are resolved.
  • The default refinement level r is given by TemplateBox[{{{InterpretationBox[{log, _, DocumentationBuild`Utils`Private`Parenth[2]}, Log2, AutoDelete -> True], (, n, )}, +, {1, /, 2}}}, Floor], where is the minimum dimension of data.  »
  • The tree of wavelet coefficients at level consists of coarse coefficients and detail coefficients , with representing the input data.
  • The forward transform is given by and , where is the filter length for the corresponding wspec and is the length of input data.  »
  • The inverse transform is given by .  »
  • The are lowpass filter coefficients and are highpass filter coefficients that are defined for each wavelet family.
  • The dimensions of and are the same as input data dimensions.
  • The following options can be given:
  • MethodAutomaticmethod to use
    WorkingPrecisionMachinePrecisionprecision to use in internal computations
  • StationaryWaveletTransform uses periodic padding of data.
  • InverseWaveletTransform gives the inverse transform.

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

Compute a stationary wavelet transform using the HaarWavelet:

In[1]:=
Click for copyable input
Out[1]=

Use Normal to view all coefficients:

In[2]:=
Click for copyable input
Out[2]=

Transform an Image object:

In[1]:=
Click for copyable input
Out[1]=

Use to extract coefficient images:

In[2]:=
Click for copyable input
Out[2]=

Compute the inverse transform:

In[3]:=
Click for copyable input
Out[3]=

Transform a sampled Sound object:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=
Introduced in 2010
(8.0)