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?
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.
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