2D DWT computation order In 2D the discrete wavelet transform (DWT) of an image using lifting based 5/3 filter, if I perform a row-wise operation first then perform column-wise operation then I will get 4 sub-band LL, LH and HL and HH.


During reconstruction, that is IDWT, should I maintain the order in reverse direction that is column first and then row? 
Or any order I can maintain? 
In JPEG 2000 there is no order information found in the header. Then how I can main the order during reconstruction?
For each single level of a isotropic or square DWT, the row/column order is not important.  Note however that there exists an alternative decomposition, termed anisotropic, rectangular, that does all rows first, then all columns (or the converse) which results in a different subband organization. This is described in the overview of 2D wavelets: A panorama on Multiscale Geometric Representations (arxiv) in Section 3: 2.3.2. Separable orthogonal wavelets.

[EDIT: Added references to related questions]


2D DWT Image Issue
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2D DWT computation order