Compute MxNE with time-frequency sparse priorΒΆ

The TF-MxNE solver is a distributed inverse method (like dSPM or sLORETA) that promotes focal (sparse) sources (such as dipole fitting techniques). The benefit of this approach is that:

  • it is spatio-temporal without assuming stationarity (sources properties can vary over time)
  • activations are localized in space, time and frequency in one step.
  • with a built-in filtering process based on a short time Fourier transform (STFT), data does not need to be low passed (just high pass to make the signals zero mean).
  • the solver solves a convex optimization problem, hence cannot be trapped in local minima.


A. Gramfort, D. Strohmeier, J. Haueisen, M. Hamalainen, M. Kowalski Time-Frequency Mixed-Norm Estimates: Sparse M/EEG imaging with non-stationary source activations Neuroimage, Volume 70, 15 April 2013, Pages 410-422, ISSN 1053-8119, DOI: 10.1016/j.neuroimage.2012.12.051.

A. Gramfort, D. Strohmeier, J. Haueisen, M. Hamalainen, M. Kowalski Functional Brain Imaging with M/EEG Using Structured Sparsity in Time-Frequency Dictionaries Proceedings Information Processing in Medical Imaging Lecture Notes in Computer Science, 2011, Volume 6801/2011, 600-611, DOI: 10.1007/978-3-642-22092-0_49

# Author: Alexandre Gramfort <>
# License: BSD (3-clause)

import mne
from mne.datasets import sample
from mne.minimum_norm import make_inverse_operator, apply_inverse
from mne.inverse_sparse import tf_mixed_norm
from mne.viz import plot_sparse_source_estimates


data_path = sample.data_path()
subjects_dir = data_path + '/subjects'
fwd_fname = data_path + '/MEG/sample/sample_audvis-meg-eeg-oct-6-fwd.fif'
ave_fname = data_path + '/MEG/sample/sample_audvis-no-filter-ave.fif'
cov_fname = data_path + '/MEG/sample/sample_audvis-shrunk-cov.fif'

# Read noise covariance matrix
cov = mne.read_cov(cov_fname)

# Handling average file
condition = 'Left visual'
evoked = mne.read_evokeds(ave_fname, condition=condition, baseline=(None, 0))
evoked = mne.pick_channels_evoked(evoked)
# We make the window slightly larger than what you'll eventually be interested
# in ([-0.05, 0.3]) to avoid edge effects.
evoked.crop(tmin=-0.1, tmax=0.4)

# Handling forward solution
forward = mne.read_forward_solution(fwd_fname, force_fixed=False,

Run solver

# alpha_space regularization parameter is between 0 and 100 (100 is high)
alpha_space = 50.  # spatial regularization parameter
# alpha_time parameter promotes temporal smoothness
# (0 means no temporal regularization)
alpha_time = 1.  # temporal regularization parameter

loose, depth = 0.2, 0.9  # loose orientation & depth weighting

# Compute dSPM solution to be used as weights in MxNE
inverse_operator = make_inverse_operator(, forward, cov,
                                         loose=loose, depth=depth)
stc_dspm = apply_inverse(evoked, inverse_operator, lambda2=1. / 9.,

# Compute TF-MxNE inverse solution
stc, residual = tf_mixed_norm(evoked, forward, cov, alpha_space, alpha_time,
                              loose=loose, depth=depth, maxit=200, tol=1e-4,
                              weights=stc_dspm, weights_min=8., debias=True,
                              wsize=16, tstep=4, window=0.05,

# Crop to remove edges
stc.crop(tmin=-0.05, tmax=0.3)
evoked.crop(tmin=-0.05, tmax=0.3)
residual.crop(tmin=-0.05, tmax=0.3)

# Show the evoked response and the residual for gradiometers
ylim = dict(grad=[-120, 120])
evoked.pick_types(meg='grad', exclude='bads')
evoked.plot(titles=dict(grad='Evoked Response: Gradiometers'), ylim=ylim,

residual.pick_types(meg='grad', exclude='bads')
residual.plot(titles=dict(grad='Residuals: Gradiometers'), ylim=ylim,
  • ../../_images/sphx_glr_plot_time_frequency_mixed_norm_inverse_001.png
  • ../../_images/sphx_glr_plot_time_frequency_mixed_norm_inverse_002.png

View in 2D and 3D (“glass” brain like 3D plot)

plot_sparse_source_estimates(forward['src'], stc, bgcolor=(1, 1, 1),
                             opacity=0.1, fig_name="TF-MxNE (cond %s)"
                             % condition, modes=['sphere'], scale_factors=[1.])

time_label = 'TF-MxNE time=%0.2f ms'
clim = dict(kind='value', lims=[10e-9, 15e-9, 20e-9])
brain = stc.plot('sample', 'inflated', 'rh', clim=clim, time_label=time_label,
                 smoothing_steps=5, subjects_dir=subjects_dir)
brain.add_label("V1", color="yellow", scalar_thresh=.5, borders=True)
brain.add_label("V2", color="red", scalar_thresh=.5, borders=True)
  • ../../_images/sphx_glr_plot_time_frequency_mixed_norm_inverse_003.png
  • ../../_images/sphx_glr_plot_time_frequency_mixed_norm_inverse_001.png
  • ../../_images/sphx_glr_plot_time_frequency_mixed_norm_inverse_002.png

Script output:

Updating smoothing matrix, be patient..
Smoothing matrix creation, step 1
Smoothing matrix creation, step 2
Smoothing matrix creation, step 3
Smoothing matrix creation, step 4
Smoothing matrix creation, step 5
colormap: fmin=1.00e-08 fmid=1.50e-08 fmax=2.00e-08 transparent=1

Total running time of the script: (0 minutes 13.233 seconds)

Download Python source code: