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Yesterday I asked about how to extract 2D DFT matrix for a vectorized image. Today my question is how can I extract 2D DWT matrix for a vectorized image. Fourier transform have this property that rows of the image are transformed first, than columns are transformed. Is there a similiar property for discrete wavelet transform such that 1D DWT matrix can be utilized for 2D DWT?

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For only one level on both direction, the classical DWT schemes are applied separately (rows then columns, or colums then rows).

For more levels, there exist two schemes:

  • one interleaving decompositions: row, col, row, col, etc. (also called non-separable/square/non-standard/isotropic/Mallat),
  • one on all rows, then all colums (also called separable/rectangle/standard/anisotropic/tensor).

The second one only deserves the "fully separable" mention.

References to related questions:

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