Q:

discrete wavelet transform matrix for vectorized image

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? 

A:

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:

2D DWT Image Issue
What is the correct order of operations for a 2D Haar wavelet decomposition?
2D DWT computation order

