Orthogonal Tensor Parameter (Moment) Maps

[bcmcpher]

Description

I'm interested in working with a recently reported set of tensor derivatives that currently have an unclear path to creation with dipy.

Specifically, I want to work with the tensor parameter maps reported here:
https://www.sciencedirect.com/science/article/pii/S0197458020304310

Briefly, the tensor eigenvalues are summarized in 3 orthogonal metrics (mean diffusivity, MD; norm of anisotropy, NA; mode of anisotropy, MO) that describe the eigenvalue moments. Knowing MD already existed, I was hoping to contribute code to estimate the other 2.

However, after digging into what is currently available, I found that the components / operations needed exist already using a different notation from this paper:
https://onlinelibrary.wiley.com/doi/full/10.1002/mrm.20741

I have a branch on my fork that adds an named function for creating NA in a way similar to existing metrics, as none of the current methods are equivalent to that map (MD / MO already exist). However, the notation from the reference does not match the existing documentation, so I'm unsure how to document it.

I could also see this gap being handled with a new Documentation page detailing how to use the existing functions / notation to create the NA map instead of adding a new function for it.

I'm willing to contribute either (or both), I just need to know what would be preferred.

Adding @arokem, this is what I mentioned at the OHBM hackathon.

[skoudoro]

Hi @bcmcpher,

Thank you for request.

I looked at the commit in your branch and I am personally fine with both options.

The contribution should be in 2 distinct PRs. Concerning the documentation, I think you just need to update the DTI tutorial by adding and explaining those new parameters

[bcmcpher]

OK, I'll work up a PR with the some additional documentation as well.

I thought of this as a new "Moments of the tensor" tutorial that would reuse a big part of the DTI tutorial, but it could probably be integrated into the existing tutorial doc.

The "challenge" that tripped me up was catching the different notation between the current reference and the new paper - they're the same equations but have different notations. With that reconciled it shouldn't be too much to add.