Compute sparse inverse solution with mixed norm: MxNE and irMxNEΒΆ

Runs (ir)MxNE (L1/L2 or L0.5/L2 mixed norm) inverse solver. L0.5/L2 is done with irMxNE which allows for sparser source estimates with less amplitude bias due to the non-convexity of the L0.5/L2 mixed norm penalty.

See Gramfort A., Kowalski M. and Hamalainen, M, Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods, Physics in Medicine and Biology, 2012

Strohmeier D., Haueisen J., and Gramfort A.: Improved MEG/EEG source localization with reweighted mixed-norms, 4th International Workshop on Pattern Recognition in Neuroimaging, Tuebingen, 2014 DOI: 10.1109/PRNI.2014.6858545

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

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


data_path = sample.data_path()
fwd_fname = data_path + '/MEG/sample/sample_audvis-meg-eeg-oct-6-fwd.fif'
ave_fname = data_path + '/MEG/sample/sample_audvis-ave.fif'
cov_fname = data_path + '/MEG/sample/sample_audvis-shrunk-cov.fif'
subjects_dir = data_path + '/subjects'

# Read noise covariance matrix
cov = mne.read_cov(cov_fname)
# Handling average file
condition = 'Left Auditory'
evoked = mne.read_evokeds(ave_fname, condition=condition, baseline=(None, 0))
evoked.crop(tmin=0, tmax=0.3)
# Handling forward solution
forward = mne.read_forward_solution(fwd_fname, surf_ori=True)

ylim = dict(eeg=[-10, 10], grad=[-400, 400], mag=[-600, 600])
evoked.plot(ylim=ylim, proj=True)

Run solver

alpha = 50  # regularization parameter between 0 and 100 (100 is high)
loose, depth = 0.2, 0.9  # loose orientation & depth weighting
n_mxne_iter = 10  # if > 1 use L0.5/L2 reweighted mixed norm solver
# if n_mxne_iter > 1 dSPM weighting can be avoided.

# Compute dSPM solution to be used as weights in MxNE
inverse_operator = make_inverse_operator(, forward, cov,
                                         loose=None, depth=depth, fixed=True)
stc_dspm = apply_inverse(evoked, inverse_operator, lambda2=1. / 9.,

# Compute (ir)MxNE inverse solution
stc, residual = mixed_norm(evoked, forward, cov, alpha, loose=loose,
                           depth=depth, maxit=3000, tol=1e-4,
                           active_set_size=10, debias=True, weights=stc_dspm,
                           weights_min=8., n_mxne_iter=n_mxne_iter,
residual.plot(ylim=ylim, proj=True)

Script output:

Convergence reached after 7 reweightings!

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

plot_sparse_source_estimates(forward['src'], stc, bgcolor=(1, 1, 1),
                             fig_name="MxNE (cond %s)" % condition,

# and on the fsaverage brain after morphing
stc_fsaverage = stc.morph(subject_from='sample', subject_to='fsaverage',
                          grade=None, sparse=True, subjects_dir=subjects_dir)
src_fsaverage_fname = subjects_dir + '/fsaverage/bem/fsaverage-ico-5-src.fif'
src_fsaverage = mne.read_source_spaces(src_fsaverage_fname)

plot_sparse_source_estimates(src_fsaverage, stc_fsaverage, bgcolor=(1, 1, 1),
  • ../../_images/sphx_glr_plot_mixed_norm_inverse_003.png
  • ../../_images/sphx_glr_plot_mixed_norm_inverse_004.png
  • ../../_images/sphx_glr_plot_mixed_norm_inverse_002.png
  • ../../_images/sphx_glr_plot_mixed_norm_inverse_003.png

Total running time of the script: (0 minutes 10.602 seconds)

Download Python source code: