Compute a sparse inverse solution using the Gamma-Map empirical Bayesian methodΒΆ

See Wipf et al. “A unified Bayesian framework for MEG/EEG source imaging.” NeuroImage, vol. 44, no. 3, pp. 947?66, Mar. 2009.

  • ../../_images/sphx_glr_plot_gamma_map_inverse_001.png
  • ../../_images/sphx_glr_plot_gamma_map_inverse_002.png
  • ../../_images/sphx_glr_plot_gamma_map_inverse_003.png
  • ../../_images/sphx_glr_plot_gamma_map_inverse_004.png

Out:

Reading /home/ubuntu/mne_data/MNE-sample-data/MEG/sample/sample_audvis-ave.fif ...
    Read a total of 4 projection items:
        PCA-v1 (1 x 102) active
        PCA-v2 (1 x 102) active
        PCA-v3 (1 x 102) active
        Average EEG reference (1 x 60) active
    Found the data of interest:
        t =    -199.80 ...     499.49 ms (Left visual)
        0 CTF compensation matrices available
        nave = 67 - aspect type = 100
Projections have already been applied. Setting proj attribute to True.
No baseline correction applied
Applying baseline correction (mode: mean)
Reading forward solution from /home/ubuntu/mne_data/MNE-sample-data/MEG/sample/sample_audvis-meg-eeg-oct-6-fwd.fif...
    Reading a source space...
    Computing patch statistics...
    Patch information added...
    Distance information added...
    [done]
    Reading a source space...
    Computing patch statistics...
    Patch information added...
    Distance information added...
    [done]
    2 source spaces read
    Desired named matrix (kind = 3523) not available
    Read MEG forward solution (7498 sources, 306 channels, free orientations)
    Desired named matrix (kind = 3523) not available
    Read EEG forward solution (7498 sources, 60 channels, free orientations)
    MEG and EEG forward solutions combined
    Source spaces transformed to the forward solution coordinate frame
    Converting to surface-based source orientations...
    Average patch normals will be employed in the rotation to the local surface coordinates....
[done]
    366 x 366 full covariance (kind = 1) found.
    Read a total of 4 projection items:
        PCA-v1 (1 x 102) active
        PCA-v2 (1 x 102) active
        PCA-v3 (1 x 102) active
        Average EEG reference (1 x 60) active
8 projection items activated
    EEG regularization : 0.1
    Created an SSP operator for EEG (dimension = 1)
    MAG regularization : 0.1
    Created an SSP operator for MAG (dimension = 3)
    GRAD regularization : 0.1
Computing inverse operator with 364 channels.
    Created an SSP operator (subspace dimension = 4)
estimated rank (mag + grad): 302
Setting small MEG eigenvalues to zero.
Not doing PCA for MEG.
estimated rank (eeg): 58
Setting small EEG eigenvalues to zero.
Not doing PCA for EEG.
Reducing data rank to 360
Total rank is 360
Whitening lead field matrix.
Applying loose dipole orientations. Loose value of 0.2.
Whitening data matrix.
Iteration: 0     active set size: 22494  convergence: 9.053e-01
Iteration: 1     active set size: 22494  convergence: 6.699e-01
Iteration: 2     active set size: 22494  convergence: 5.061e-01
Iteration: 3     active set size: 22494  convergence: 5.198e-01
Iteration: 4     active set size: 22494  convergence: 5.746e-01
Iteration: 5     active set size: 22494  convergence: 5.490e-01
Iteration: 6     active set size: 22494  convergence: 4.253e-01
Iteration: 7     active set size: 22494  convergence: 2.763e-01
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Iteration: 692   active set size: 12     convergence: 3.299e-06
Iteration: 693   active set size: 12     convergence: 3.281e-06
Iteration: 694   active set size: 12     convergence: 3.263e-06
Iteration: 695   active set size: 12     convergence: 3.246e-06
Iteration: 696   active set size: 12     convergence: 3.229e-06
Iteration: 697   active set size: 12     convergence: 3.212e-06
Iteration: 698   active set size: 12     convergence: 3.194e-06
Iteration: 699   active set size: 12     convergence: 3.177e-06
Iteration: 700   active set size: 12     convergence: 3.160e-06
Iteration: 701   active set size: 12     convergence: 3.144e-06
Iteration: 702   active set size: 12     convergence: 3.127e-06
Iteration: 703   active set size: 12     convergence: 3.110e-06
Iteration: 704   active set size: 12     convergence: 3.094e-06
Iteration: 705   active set size: 12     convergence: 3.077e-06
Iteration: 706   active set size: 12     convergence: 3.061e-06
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Iteration: 708   active set size: 12     convergence: 3.028e-06
Iteration: 709   active set size: 12     convergence: 3.012e-06
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Iteration: 711   active set size: 12     convergence: 2.980e-06
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Iteration: 715   active set size: 12     convergence: 2.917e-06
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Iteration: 718   active set size: 12     convergence: 2.871e-06
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Iteration: 720   active set size: 12     convergence: 2.840e-06
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Iteration: 723   active set size: 12     convergence: 2.795e-06
Iteration: 724   active set size: 12     convergence: 2.780e-06
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Iteration: 728   active set size: 12     convergence: 2.722e-06
Iteration: 729   active set size: 12     convergence: 2.707e-06
Iteration: 730   active set size: 12     convergence: 2.693e-06
Iteration: 731   active set size: 12     convergence: 2.678e-06
Iteration: 732   active set size: 12     convergence: 2.664e-06
Iteration: 733   active set size: 12     convergence: 2.650e-06
Iteration: 734   active set size: 12     convergence: 2.636e-06
Iteration: 735   active set size: 12     convergence: 2.622e-06
Iteration: 736   active set size: 12     convergence: 2.608e-06
Iteration: 737   active set size: 12     convergence: 2.594e-06
Iteration: 738   active set size: 12     convergence: 2.580e-06
Iteration: 739   active set size: 12     convergence: 2.567e-06
Iteration: 740   active set size: 12     convergence: 2.553e-06
Iteration: 741   active set size: 12     convergence: 2.539e-06
Iteration: 742   active set size: 12     convergence: 2.526e-06
Iteration: 743   active set size: 12     convergence: 2.512e-06
Iteration: 744   active set size: 12     convergence: 2.499e-06
Iteration: 745   active set size: 12     convergence: 2.486e-06
Iteration: 746   active set size: 12     convergence: 2.473e-06
Iteration: 747   active set size: 12     convergence: 2.459e-06
Iteration: 748   active set size: 12     convergence: 2.446e-06
Iteration: 749   active set size: 12     convergence: 2.433e-06
Iteration: 750   active set size: 12     convergence: 2.420e-06
Iteration: 751   active set size: 12     convergence: 2.408e-06
Iteration: 752   active set size: 12     convergence: 2.395e-06
Iteration: 753   active set size: 12     convergence: 2.382e-06
Iteration: 754   active set size: 12     convergence: 2.369e-06
Iteration: 755   active set size: 12     convergence: 2.357e-06
Iteration: 756   active set size: 12     convergence: 2.344e-06
Iteration: 757   active set size: 12     convergence: 2.332e-06
Iteration: 758   active set size: 12     convergence: 2.319e-06
Iteration: 759   active set size: 12     convergence: 2.307e-06
Iteration: 760   active set size: 12     convergence: 2.295e-06
Iteration: 761   active set size: 12     convergence: 2.283e-06
Iteration: 762   active set size: 12     convergence: 2.270e-06
Iteration: 763   active set size: 12     convergence: 2.258e-06
Iteration: 764   active set size: 12     convergence: 2.246e-06
Iteration: 765   active set size: 12     convergence: 2.234e-06
Iteration: 766   active set size: 12     convergence: 2.223e-06
Iteration: 767   active set size: 12     convergence: 2.211e-06
Iteration: 768   active set size: 12     convergence: 2.199e-06
Iteration: 769   active set size: 12     convergence: 2.187e-06
Iteration: 770   active set size: 12     convergence: 2.176e-06
Iteration: 771   active set size: 12     convergence: 2.164e-06
Iteration: 772   active set size: 12     convergence: 2.153e-06
Iteration: 773   active set size: 12     convergence: 2.141e-06
Iteration: 774   active set size: 12     convergence: 2.130e-06
Iteration: 775   active set size: 12     convergence: 2.119e-06
Iteration: 776   active set size: 12     convergence: 2.107e-06
Iteration: 777   active set size: 12     convergence: 2.096e-06
Iteration: 778   active set size: 12     convergence: 2.085e-06
Iteration: 779   active set size: 12     convergence: 2.074e-06
Iteration: 780   active set size: 12     convergence: 2.063e-06
Iteration: 781   active set size: 12     convergence: 2.052e-06
Iteration: 782   active set size: 12     convergence: 2.041e-06
Iteration: 783   active set size: 12     convergence: 2.030e-06
Iteration: 784   active set size: 12     convergence: 2.019e-06
Iteration: 785   active set size: 12     convergence: 2.009e-06
Iteration: 786   active set size: 12     convergence: 1.998e-06
Iteration: 787   active set size: 12     convergence: 1.987e-06
Iteration: 788   active set size: 12     convergence: 1.977e-06
Iteration: 789   active set size: 12     convergence: 1.966e-06
Iteration: 790   active set size: 12     convergence: 1.956e-06
Iteration: 791   active set size: 12     convergence: 1.946e-06
Iteration: 792   active set size: 12     convergence: 1.935e-06
Iteration: 793   active set size: 12     convergence: 1.925e-06
Iteration: 794   active set size: 12     convergence: 1.915e-06
Iteration: 795   active set size: 12     convergence: 1.905e-06
Iteration: 796   active set size: 12     convergence: 1.894e-06
Iteration: 797   active set size: 12     convergence: 1.884e-06
Iteration: 798   active set size: 12     convergence: 1.874e-06
Iteration: 799   active set size: 12     convergence: 1.864e-06
Iteration: 800   active set size: 12     convergence: 1.855e-06
Iteration: 801   active set size: 12     convergence: 1.845e-06
Iteration: 802   active set size: 12     convergence: 1.835e-06
Iteration: 803   active set size: 12     convergence: 1.825e-06
Iteration: 804   active set size: 12     convergence: 1.815e-06
Iteration: 805   active set size: 12     convergence: 1.806e-06
Iteration: 806   active set size: 12     convergence: 1.796e-06
Iteration: 807   active set size: 12     convergence: 1.787e-06
Iteration: 808   active set size: 12     convergence: 1.777e-06
Iteration: 809   active set size: 12     convergence: 1.768e-06
Iteration: 810   active set size: 12     convergence: 1.758e-06
Iteration: 811   active set size: 12     convergence: 1.749e-06
Iteration: 812   active set size: 12     convergence: 1.740e-06
Iteration: 813   active set size: 12     convergence: 1.731e-06
Iteration: 814   active set size: 12     convergence: 1.721e-06
Iteration: 815   active set size: 12     convergence: 1.712e-06
Iteration: 816   active set size: 12     convergence: 1.703e-06
Iteration: 817   active set size: 12     convergence: 1.694e-06
Iteration: 818   active set size: 12     convergence: 1.685e-06
Iteration: 819   active set size: 12     convergence: 1.676e-06
Iteration: 820   active set size: 12     convergence: 1.667e-06
Iteration: 821   active set size: 12     convergence: 1.659e-06
Iteration: 822   active set size: 12     convergence: 1.650e-06
Iteration: 823   active set size: 12     convergence: 1.641e-06
Iteration: 824   active set size: 12     convergence: 1.632e-06
Iteration: 825   active set size: 12     convergence: 1.624e-06
Iteration: 826   active set size: 12     convergence: 1.615e-06
Iteration: 827   active set size: 12     convergence: 1.606e-06
Iteration: 828   active set size: 12     convergence: 1.598e-06
Iteration: 829   active set size: 12     convergence: 1.589e-06
Iteration: 830   active set size: 12     convergence: 1.581e-06
Iteration: 831   active set size: 12     convergence: 1.573e-06
Iteration: 832   active set size: 12     convergence: 1.564e-06
Iteration: 833   active set size: 12     convergence: 1.556e-06
Iteration: 834   active set size: 12     convergence: 1.548e-06
Iteration: 835   active set size: 12     convergence: 1.540e-06
Iteration: 836   active set size: 12     convergence: 1.531e-06
Iteration: 837   active set size: 12     convergence: 1.523e-06
Iteration: 838   active set size: 12     convergence: 1.515e-06
Iteration: 839   active set size: 12     convergence: 1.507e-06
Iteration: 840   active set size: 12     convergence: 1.499e-06
Iteration: 841   active set size: 12     convergence: 1.491e-06
Iteration: 842   active set size: 12     convergence: 1.483e-06
Iteration: 843   active set size: 12     convergence: 1.475e-06
Iteration: 844   active set size: 12     convergence: 1.468e-06
Iteration: 845   active set size: 12     convergence: 1.460e-06
Iteration: 846   active set size: 12     convergence: 1.452e-06
Iteration: 847   active set size: 12     convergence: 1.444e-06
Iteration: 848   active set size: 12     convergence: 1.437e-06
Iteration: 849   active set size: 12     convergence: 1.429e-06
Iteration: 850   active set size: 12     convergence: 1.422e-06
Iteration: 851   active set size: 12     convergence: 1.414e-06
Iteration: 852   active set size: 12     convergence: 1.407e-06
Iteration: 853   active set size: 12     convergence: 1.399e-06
Iteration: 854   active set size: 12     convergence: 1.392e-06
Iteration: 855   active set size: 12     convergence: 1.384e-06
Iteration: 856   active set size: 12     convergence: 1.377e-06
Iteration: 857   active set size: 12     convergence: 1.370e-06
Iteration: 858   active set size: 12     convergence: 1.362e-06
Iteration: 859   active set size: 12     convergence: 1.355e-06
Iteration: 860   active set size: 12     convergence: 1.348e-06
Iteration: 861   active set size: 12     convergence: 1.341e-06
Iteration: 862   active set size: 12     convergence: 1.334e-06
Iteration: 863   active set size: 12     convergence: 1.327e-06
Iteration: 864   active set size: 12     convergence: 1.320e-06
Iteration: 865   active set size: 12     convergence: 1.313e-06
Iteration: 866   active set size: 12     convergence: 1.306e-06
Iteration: 867   active set size: 12     convergence: 1.299e-06
Iteration: 868   active set size: 12     convergence: 1.292e-06
Iteration: 869   active set size: 12     convergence: 1.285e-06
Iteration: 870   active set size: 12     convergence: 1.278e-06
Iteration: 871   active set size: 12     convergence: 1.271e-06
Iteration: 872   active set size: 12     convergence: 1.265e-06
Iteration: 873   active set size: 12     convergence: 1.258e-06
Iteration: 874   active set size: 12     convergence: 1.251e-06
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Iteration: 876   active set size: 12     convergence: 1.238e-06
Iteration: 877   active set size: 12     convergence: 1.232e-06
Iteration: 878   active set size: 12     convergence: 1.225e-06
Iteration: 879   active set size: 12     convergence: 1.219e-06
Iteration: 880   active set size: 12     convergence: 1.212e-06
Iteration: 881   active set size: 12     convergence: 1.206e-06
Iteration: 882   active set size: 12     convergence: 1.199e-06
Iteration: 883   active set size: 12     convergence: 1.193e-06
Iteration: 884   active set size: 12     convergence: 1.187e-06
Iteration: 885   active set size: 12     convergence: 1.180e-06
Iteration: 886   active set size: 12     convergence: 1.174e-06
Iteration: 887   active set size: 12     convergence: 1.168e-06
Iteration: 888   active set size: 12     convergence: 1.162e-06
Iteration: 889   active set size: 12     convergence: 1.156e-06
Iteration: 890   active set size: 12     convergence: 1.149e-06
Iteration: 891   active set size: 12     convergence: 1.143e-06
Iteration: 892   active set size: 12     convergence: 1.137e-06
Iteration: 893   active set size: 12     convergence: 1.131e-06
Iteration: 894   active set size: 12     convergence: 1.125e-06
Iteration: 895   active set size: 12     convergence: 1.119e-06
Iteration: 896   active set size: 12     convergence: 1.113e-06
Iteration: 897   active set size: 12     convergence: 1.108e-06
Iteration: 898   active set size: 12     convergence: 1.102e-06
Iteration: 899   active set size: 12     convergence: 1.096e-06
Iteration: 900   active set size: 12     convergence: 1.090e-06
Iteration: 901   active set size: 12     convergence: 1.084e-06
Iteration: 902   active set size: 12     convergence: 1.079e-06
Iteration: 903   active set size: 12     convergence: 1.073e-06
Iteration: 904   active set size: 12     convergence: 1.067e-06
Iteration: 905   active set size: 12     convergence: 1.061e-06
Iteration: 906   active set size: 12     convergence: 1.056e-06
Iteration: 907   active set size: 12     convergence: 1.050e-06
Iteration: 908   active set size: 12     convergence: 1.045e-06
Iteration: 909   active set size: 12     convergence: 1.039e-06
Iteration: 910   active set size: 12     convergence: 1.034e-06
Iteration: 911   active set size: 12     convergence: 1.028e-06
Iteration: 912   active set size: 12     convergence: 1.023e-06
Iteration: 913   active set size: 12     convergence: 1.017e-06
Iteration: 914   active set size: 12     convergence: 1.012e-06
Iteration: 915   active set size: 12     convergence: 1.007e-06
Iteration: 916   active set size: 12     convergence: 1.001e-06
Iteration: 917   active set size: 12     convergence: 9.960e-07

Convergence reached !

4 projection items deactivated
Created an SSP operator (subspace dimension = 4)
4 projection items activated
SSP projectors applied...
0 projection items deactivated
combining the current components...
Total number of active sources: 4

# Author: Martin Luessi <mluessi@nmr.mgh.harvard.edu>
#
# License: BSD (3-clause)

import numpy as np

import mne
from mne.datasets import sample
from mne.inverse_sparse import gamma_map
from mne.viz import plot_sparse_source_estimates

print(__doc__)

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

# Read the evoked response and crop it
condition = 'Left visual'
evoked = mne.read_evokeds(evoked_fname, condition=condition,
                          baseline=(None, 0))
evoked.crop(tmin=-50e-3, tmax=300e-3)

# Read the forward solution
forward = mne.read_forward_solution(fwd_fname, surf_ori=True,
                                    force_fixed=False)

# Read noise noise covariance matrix and regularize it
cov = mne.read_cov(cov_fname)
cov = mne.cov.regularize(cov, evoked.info)

# Run the Gamma-MAP method
alpha = 0.5
stc, residual = gamma_map(evoked, forward, cov, alpha, xyz_same_gamma=True,
                          return_residual=True)

# View in 2D and 3D ("glass" brain like 3D plot)

# Show the sources as spheres scaled by their strength
scale_factors = np.max(np.abs(stc.data), axis=1)
scale_factors = 0.5 * (1 + scale_factors / np.max(scale_factors))

plot_sparse_source_estimates(
    forward['src'], stc, bgcolor=(1, 1, 1),
    modes=['sphere'], opacity=0.1, scale_factors=(scale_factors, None),
    fig_name="Gamma-MAP")

# 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,
            proj=True)

residual.pick_types(meg='grad', exclude='bads')
residual.plot(titles=dict(grad='Residuals Gradiometers'), ylim=ylim,
              proj=True)

Total running time of the script: ( 1 minutes 8.695 seconds)

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