Wolfram Language & System 11.0 (2016)|Legacy Documentation

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gives the inverse wavelet transform of a DiscreteWaveletData object dwd.

gives the inverse transform using the wavelet wave.

gives the inverse transform from the wavelet coefficients specified by wind.

Details and OptionsDetails and Options

  • InverseWaveletTransform computes the inverse transform of discrete forward transforms such as DiscreteWaveletTransform etc.
  • The possible wavelets wave are the same as for the forward wavelet transforms.
  • The default wave is Automatic, which is taken to be dwd["Wavelet"].
  • The possible specifications for wind are the same as used by DiscreteWaveletData.
  • The default wind is Automatic, which is taken to be dwd["BasisIndex"].
  • InverseWaveletTransform[dwd,wave,wind] computes the inverse transform using only the wavelet coefficients specified by wind; other coefficients are set to be zero.
  • The inverse transform works recursively by computing coefficients with wavelet index {w1,,wn-1} from coefficients with wavelet index {w1,,wn-1,wn}.
  • An explicit wind specification needs to be consistent. A wind specification is consistent if for each {w1,,wn} that is included no {w1,,wk} for k<n is included.
  • InverseWaveletTransform[dwd,wave,r] can be used to inverse transform the r lowest levels of the wavelet tree.
  • The default level r is given by the number of refinement levels n in dwd. With r<n a new DiscreteWaveletData object is returned with n-r refinement levels.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Perform a discrete wavelet transform:

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Inverse transform recovers the original data:

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DiscreteWaveletData representing modified wavelet image coefficients:

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Inverse transform gives filtered image:

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Introduced in 2010