Compute iterative reweighted TF-MxNE with multiscale time-frequency dictionary

The iterative reweighted TF-MxNE solver is a distributed inverse method based on the TF-MxNE solver, which promotes focal (sparse) sources [1]. The benefits of this approach are that:

• it is spatio-temporal without assuming stationarity (source properties can vary over time),

• activations are localized in space, time, and frequency in one step,

• the solver uses non-convex penalties in the TF domain, which results in a solution less biased towards zero than when simple TF-MxNE is used,

• using a multiscale dictionary allows to capture short transient activations along with slower brain waves [2].

# Author: Mathurin Massias <mathurin.massias@gmail.com>
#         Yousra Bekhti <yousra.bekhti@gmail.com>
#         Daniel Strohmeier <daniel.strohmeier@tu-ilmenau.de>
#         Alexandre Gramfort <alexandre.gramfort@inria.fr>
#
# License: BSD-3-Clause
# Copyright the MNE-Python contributors.

import mne
from mne.datasets import somato
from mne.inverse_sparse import make_stc_from_dipoles, tf_mixed_norm
from mne.viz import plot_sparse_source_estimates

print(__doc__)

Load somatosensory MEG data

data_path = somato.data_path()
subject = "01"
task = "somato"
raw_fname = data_path / f"sub-{subject}" / "meg" / f"sub-{subject}_task-{task}_meg.fif"
fwd_fname = (
    data_path / "derivatives" / f"sub-{subject}" / f"sub-{subject}_task-{task}-fwd.fif"
)

# Read evoked
raw = mne.io.read_raw_fif(raw_fname)
raw.pick(picks=["meg", "eog", "stim"])
events = mne.find_events(raw, stim_channel="STI 014")

reject = dict(grad=4000e-13, eog=350e-6)
event_id, tmin, tmax = dict(unknown=1), -0.5, 0.5
epochs = mne.Epochs(
    raw, events, event_id, tmin, tmax, reject=reject, baseline=(None, 0)
)
evoked = epochs.average()

evoked.crop(tmin=0.0, tmax=0.2)

# Compute noise covariance matrix
cov = mne.compute_covariance(epochs, rank="info", tmax=0.0)
del epochs, raw

# Handling forward solution
forward = mne.read_forward_solution(fwd_fname)

Opening raw data file /home/circleci/mne_data/MNE-somato-data/sub-01/meg/sub-01_task-somato_meg.fif...
    Range : 237600 ... 506999 =    791.189 ...  1688.266 secs
Ready.
111 events found on stim channel STI 014
Event IDs: [1]
Not setting metadata
111 matching events found
Setting baseline interval to [-0.49948803289596966, 0.0] s
Applying baseline correction (mode: mean)
0 projection items activated
    Rejecting  epoch based on EOG : ['EOG 061']
Loading data for 111 events and 301 original time points ...
    Rejecting  epoch based on EOG : ['EOG 061']
1 bad epochs dropped
    Setting small MEG eigenvalues to zero (without PCA)
Reducing data rank from 306 -> 64
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 16610
[done]
Reading forward solution from /home/circleci/mne_data/MNE-somato-data/derivatives/sub-01/sub-01_task-somato-fwd.fif...
    Reading a source space...
    [done]
    Reading a source space...
    [done]
    2 source spaces read
    Desired named matrix (kind = 3523 (FIFF_MNE_FORWARD_SOLUTION_GRAD)) not available
    Read MEG forward solution (8155 sources, 306 channels, free orientations)
    Source spaces transformed to the forward solution coordinate frame

Run iterative reweighted multidict TF-MxNE solver

alpha, l1_ratio = 20, 0.05
loose, depth = 0.9, 1.0
# Use a multiscale time-frequency dictionary
wsize, tstep = [4, 16], [2, 4]


n_tfmxne_iter = 10
# Compute TF-MxNE inverse solution with dipole output
dipoles, residual = tf_mixed_norm(
    evoked,
    forward,
    cov,
    alpha=alpha,
    l1_ratio=l1_ratio,
    n_tfmxne_iter=n_tfmxne_iter,
    loose=loose,
    depth=depth,
    tol=1e-3,
    wsize=wsize,
    tstep=tstep,
    return_as_dipoles=True,
    return_residual=True,
)

Converting forward solution to surface orientation
    No patch info available. The standard source space normals will be employed in the rotation to the local surface coordinates....
    Converting to surface-based source orientations...
    [done]
Computing inverse operator with 306 channels.
    306 out of 306 channels remain after picking
Selected 306 channels
Creating the depth weighting matrix...
Applying loose dipole orientations to surface source spaces: 0.9
Whitening the forward solution.
Computing rank from covariance with rank=None
    Using tolerance 3.6e-12 (2.2e-16 eps * 306 dim * 53  max singular value)
    Estimated rank (mag + grad): 64
    MEG: rank 64 computed from 306 data channels with 0 projectors
    Setting small MEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Whitening data matrix.

dgap 9.89e+01 :: p_obj 289.000835 :: d_obj 190.083203 :: n_active 247

dgap 1.27e+01 :: p_obj 253.327890 :: d_obj 240.582652 :: n_active 132

    Iteration 10 :: n_active 82
    dgap 4.53e+00 :: p_obj 250.70728489607475 :: d_obj 246.18210074285165

dgap 3.18e+00 :: p_obj 250.589468 :: d_obj 247.408712 :: n_active 76

    Iteration 10 :: n_active 60
    dgap 1.82e+00 :: p_obj 250.24368799194698 :: d_obj 248.42055602514802

    Iteration 20 :: n_active 55
    dgap 1.67e+00 :: p_obj 250.09497054568965 :: d_obj 248.42055602514802

    Iteration 30 :: n_active 48
    dgap 1.57e+00 :: p_obj 249.99106679959243 :: d_obj 248.42055602514802

    Iteration 40 :: n_active 43
    dgap 1.49e+00 :: p_obj 249.93649794914268 :: d_obj 248.44246671366014

    Iteration 50 :: n_active 43
    dgap 1.08e+00 :: p_obj 249.90687133785872 :: d_obj 248.82986983079047

    Iteration 60 :: n_active 43
    dgap 8.70e-01 :: p_obj 249.8872046078418 :: d_obj 249.01722263537022

    Iteration 70 :: n_active 43
    dgap 7.24e-01 :: p_obj 249.8721073783407 :: d_obj 249.14858291086628

dgap 1.11e+00 :: p_obj 249.872107 :: d_obj 248.762424 :: n_active 43

    Iteration 10 :: n_active 44
    dgap 5.94e-01 :: p_obj 249.85401187839332 :: d_obj 249.25962912136725

dgap 5.94e-01 :: p_obj 249.854012 :: d_obj 249.259629 :: n_active 44

Convergence reached!

Iteration 1: active set size=44, E=659.867870

    Iteration 10 :: n_active 8
    dgap 4.46e+00 :: p_obj 275.04359564810875 :: d_obj 270.5878411157467

    Iteration 20 :: n_active 8
    dgap 1.87e+00 :: p_obj 274.72222975699003 :: d_obj 272.85639909989857

    Iteration 30 :: n_active 8
    dgap 8.29e-01 :: p_obj 274.6780129582929 :: d_obj 273.8492833846071

dgap 8.29e-01 :: p_obj 274.678013 :: d_obj 273.849283 :: n_active 8

Convergence reached!

Iteration 2: active set size=8, E=335.966495

    Iteration 10 :: n_active 5
    dgap 2.73e+00 :: p_obj 239.21534127692587 :: d_obj 236.48179575685523

    Iteration 20 :: n_active 5
    dgap 9.17e-01 :: p_obj 239.09550882070073 :: d_obj 238.17850381087743

    Iteration 30 :: n_active 5
    dgap 4.77e-01 :: p_obj 239.06850689155203 :: d_obj 238.59128622008313

dgap 4.77e-01 :: p_obj 239.068507 :: d_obj 238.591286 :: n_active 5

Convergence reached!

Iteration 3: active set size=5, E=298.546285

    Iteration 10 :: n_active 5
    dgap 3.06e-01 :: p_obj 223.13301276505058 :: d_obj 222.826665511768

dgap 3.06e-01 :: p_obj 223.133013 :: d_obj 222.826666 :: n_active 5

Convergence reached!

Iteration 4: active set size=5, E=295.194637
Convergence reached after 3 reweightings!
Debiasing converged after 551 iterations max(|D - D0| = 6.235946e-07 < 1.000000e-06)
[done]

Generate stc from dipoles

stc = make_stc_from_dipoles(dipoles, forward["src"])
plot_sparse_source_estimates(
    forward["src"],
    stc,
    bgcolor=(1, 1, 1),
    opacity=0.1,
    fig_name=f"irTF-MxNE (cond {evoked.comment})",
)

Converting dipoles into a SourceEstimate.
[done]
Total number of active sources: [ 81892 187503 219550 230933 241074]

Show the evoked response and the residual for gradiometers

ylim = dict(grad=[-300, 300])
evoked.copy().pick(picks="grad").plot(
    titles=dict(grad="Evoked Response: Gradiometers"), ylim=ylim
)
residual.copy().pick(picks="grad").plot(
    titles=dict(grad="Residuals: Gradiometers"), ylim=ylim
)

• 
• 

References

[1]

Daniel Strohmeier, Alexandre Gramfort, and Jens Haueisen. MEG/EEG Source Imaging with a Non-Convex Penalty in the Time-Frequency Domain. In 2015 International Workshop on Pattern Recognition in NeuroImaging, 21–24. 2015. doi:10.1109/PRNI.2015.14.

[2]

Yousra Bekhti, Daniel Strohmeier, Mainak Jas, Roland Badeau, and Alexandre Gramfort. M/EEG source localization with multi-scale time-frequency dictionaries. In Proceedings of PRNI-2016, 1–4. Trento, 2016. IEEE. doi:10.1109/PRNI.2016.7552337.