Axial to planar gradiometer transformation

[contsili]

Reference issue (if any)

Fixes #9609 .

What does this implement/fix?

• Store the canonical CTF and Neuromag sensor definitions in a txt file
• Extent interpolate_to() to MEG sensors to accommodate axial to planar gradiometer transformation (and back)
• Since interpolate_to() works similarly to interpolate_bads() I suggest we create two new functions in interpolation.py: _interpolate_to_meeg that uses the 'MNE' interpolation method

Additional information

The channel positions and orientations are adopted from fieldtrip: https://github.com/fieldtrip/fieldtrip/blob/master/template/gradiometer

I am not sure if for the interpolation we need the coil positions and orientations. For clarity: a gradiometer is ONE channel but has TWO coils. A magnetometer is ONE channel and has ONE coil.

As an expectation I have that I will plot ERPs in the ctf and neuromag format. Also I want to create topoplots like: https://www.fieldtriptoolbox.org/assets/img/tutorial/eventrelatedaveraging/figure8.png

[welcome]

Hello! 👋 Thanks for opening your first pull request here! ❤️ We will try to get back to you soon. 🚴

[larsoner]

Looks like you're making some progress, let me know when you'd like some feedback!

[contsili]

Hi @larsoner! After a while, I finally found some time :)

I think this is a good moment for some feedback.

Issues / Questions I encountered:
1. Handling ch_type when interpolating from CTF → Neuromag

My initial understanding was that when we interpolate from CTF to Neuromag, the ch_type should already be known.

This is because, CTF systems have reference sensors that should not be interpolated and Neuromag systems have gradiometers and magnetometers, so we need to know the type of each channel.

That's why I added the ch_type parameter in the .txt montage files — to explicitly specify this.

2. Scope of interpolation: only gradiometers?
In relation to (1), I assumed we would only interpolate gradiometers (i.e., axial ↔ planar), and not magnetometers.

Based on this, I thought I would input in _map_eeg_and_meg_channels would use info_from and info_to objects that contain only the gradiometer channels. This was another reason for adding the ch_type parameter in the montage.

3. Limitations of make_dig_montage
All the montages are created via make_dig_montage.

From the documentation of make_dig_montage:

 .. note::
            For custom montages without fiducials, this parameter must be set
            to ``'head'``.

I understood that for my setup (no fiducials) I should use a custom montage.

However: running montage = make_dig_montage(ch_pos=ch_pos, coord_frame="head") does not parse the ch_type or ori and my channels are read as generic EEG labels, e.g., standard_montage.ch_names[0] = 'EEG #1' etc.

4. Custom _meg() function and related problems
Because of (3), I created a custom_meg()function to parse the .txt files.

But now I run into new problems. When I run interpolate_to() :

_validate_type(sensors, DigMontage, "sensors") leads to the error: AttributeError: 'CustomMontage' object has no attribute 'get_positions'
ch_pos = sensors.get_positions().get("ch_pos", {}) leads to the error: sensors must be an instance of DigMontage, got <class 'mne.channels._standard_montage_utils._meg.<locals>.CustomMontage'> instead

5. I added _meg() inside _standard_montage_utils but am I allowed to change such private function ?

6. I am trying to follow how interpolate_to() code style and structure is already built.

However, this forces us to diverge a bit from the standard interpolate_bads recipe

One idea I had would be to encapsulate some logic in a new function interpolate_to_meeg() inside interpolation.py. Just as interpolate_bads_meeg() works inside interpolation.py. But if we do that then we need to do the same thing for the EEG part of interpolate_to()