ktaswell
commented
1 year ago After working with it some more, I think I actually may have had it correct the first time around while working on it a couple weeks ago and simply had a "wait did I mess up moment". I'll put my notes here for others to confirm/check:
When not specifying a level to transform to, Wavelets.jl automatically transforms up to maximum level.
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For the case of $n \times n \times n$ , where $n=2^k$ is dyadic, dwt function decomposes to max level $k$ leaving only 1 approximation coefficient in [1, 1, 1] position as the only remaining value with the detail coefficients for level $k$ in positions of index greater than 2 in each dimension.
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For the case of $n\times n\times m$, where $n = 2^k, m = 2^j$ with $k < j$, dwt function decomposes to max level $k$ again, however this time having $b=m/n = 2^{j-k}$ approximation coefficients, stored along the 3rd dimension which has the longest length. Making approximation coefficients stored in positions [1, 1, 1:b] and level $k$ detail coefficients stored in positions greater than 2 in dims 1 and 2, while positions greater than $b$, for dim 3.
If I have the right thinking here, please let me know.
JeffFessler
gummif
I'm trying to implement a soft thresholding method for 3D data which preserves scaling (or approximation) coefficients at each level, then soft thresholds all others. Unfortunately, I have been having trouble identifying indices which correspond to the scaling coefficients. I was trying to make sense of the detailn() and detailindex() functions and it makes sense to me for 1D condition, but I don't understand how to use these to create an index list for higher dimensions, like the 3D condition that I need.
Also to complicate further, I need to handle both dyadic cube and dyadic non-cube dimensions.
Could someone help me with this?
Thanks