[WIP, ENH] Add GODEC

[tsalo]

Closes #79. Ref #106.

@dowdlelt I know that you were able to get the GODEC implementation here working. I used that code as well, with several changes to remove redundancy and unused functions. Perhaps you could take a look at this PR?

Changes proposed in this pull request:

• Add Go Decomposition to package under tedana.decomposition.godecomp.tedgodec.
• Integrate GODEC into tedana workflow with ws_denoise argument. Still haven't added a command-line argument.
• Fix potential bug in MEDN construction within tedana.utils.io.gscontrol_mmix. I've removed this to prevent bloat in the PR. I'm going to open a separate PR ([FIX] Include ignored components in ME-DN T1c time series #125) for this potential bug fix.
• Replace label with out_dir and add out_dir argument to many functions. Removed to reduce bloat.

To do:

• Code review
• Add unit tests
• Update documentation
• Update CLI

[dowdlelt]

I looked for anything obvious, and it seems fine by me. I believe 'vn' is for variance normalization, rather than demeaning.

I am not sure there I ever actually got the python implementation working correctly, though I do recall getting close. When I brought this up on the MEICA repository I was pointed towards the T1c outputs provided by MEICA, by @prantikk here. Limited testing suggested that the T1c mimicked the characteristics of the godec output from the 2018 Power et al paper, all with less fiddling. I believe the biggest problem I ran into was in the output from the algorithm, rather than running it.

In any case, once this is tested it would be nice to compare the T1c data with the GoDec output to confirm (or not) similarities in a single dataset.

[tsalo]

Thanks for taking a look @dowdlelt. Also thanks for catching vn's meaning!

Do you know if there's any kind of citation for the minimum image regression? The Power paper (as you know) recommended GODEC or a more standard GSR (which doesn't seem to be implemented in the same way in gscontrol_raw in tedana), but I'm guessing that the minimum image regression came later.

Certainly a quantitative comparison of the recommended method from the literature (GODEC) against the new, simpler method recommended here (T1c) would be nice for anyone who wants to publish using T1c.

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On a more general note, I think this is a good opportunity to move gscontrol_mmix out of tedana.utils.io (where it definitely doesn't belong) to someplace that makes more sense. I was considering moving it to tedana.decomposition. Does that sound reasonable? Alternatively, both gscontrol_mmix and tedgodec could go into a new submodule for methods for removing widespread noise (as they were referred to in the Power paper).

[codecov]

Codecov Report

Merging #120 into master will decrease coverage by 1.64%.
The diff coverage is 13.33%.

@@            Coverage Diff            @@
##           master    #120      +/-   ##
=========================================
- Coverage   51.54%   49.9%   -1.65%     
=========================================
  Files          32      33       +1     
  Lines        1969    2058      +89     
=========================================
+ Hits         1015    1027      +12     
- Misses        954    1031      +77

Impacted Files	Coverage Δ
tedana/model/fit.py	27.71% <ø> (ø)	⬆️
tedana/io.py	35.55% <0%> (ø)	⬆️
tedana/workflows/tedana.py	14.18% <0%> (-0.2%)	⬇️
tedana/decomposition/__init__.py	100% <100%> (ø)	⬆️
tedana/decomposition/godecomp.py	12.79% <12.79%> (ø)

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[jbteves]

I remembered this PR while re-reading #79. With all of the merges there are no some conflicts. Would you mind updating this branch to be up-to-date with master?