Note

Click here to download the full example code

# Compute MNE-dSPM inverse solution on single epochs¶

Compute dSPM inverse solution on single trial epochs restricted to a brain label.

```
# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
#
# License: BSD (3-clause)
import numpy as np
import matplotlib.pyplot as plt
import mne
from mne.datasets import sample
from mne.minimum_norm import apply_inverse_epochs, read_inverse_operator
from mne.minimum_norm import apply_inverse
print(__doc__)
data_path = sample.data_path()
fname_inv = data_path + '/MEG/sample/sample_audvis-meg-oct-6-meg-inv.fif'
fname_raw = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw.fif'
fname_event = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw-eve.fif'
label_name = 'Aud-lh'
fname_label = data_path + '/MEG/sample/labels/%s.label' % label_name
event_id, tmin, tmax = 1, -0.2, 0.5
# Using the same inverse operator when inspecting single trials Vs. evoked
snr = 3.0 # Standard assumption for average data but using it for single trial
lambda2 = 1.0 / snr ** 2
method = "dSPM" # use dSPM method (could also be MNE or sLORETA)
# Load data
inverse_operator = read_inverse_operator(fname_inv)
label = mne.read_label(fname_label)
raw = mne.io.read_raw_fif(fname_raw)
events = mne.read_events(fname_event)
# Set up pick list
include = []
# Add a bad channel
raw.info['bads'] += ['EEG 053'] # bads + 1 more
# pick MEG channels
picks = mne.pick_types(raw.info, meg=True, eeg=False, stim=False, eog=True,
include=include, exclude='bads')
# Read epochs
epochs = mne.Epochs(raw, events, event_id, tmin, tmax, picks=picks,
baseline=(None, 0), reject=dict(mag=4e-12, grad=4000e-13,
eog=150e-6))
# Get evoked data (averaging across trials in sensor space)
evoked = epochs.average()
# Compute inverse solution and stcs for each epoch
# Use the same inverse operator as with evoked data (i.e., set nave)
# If you use a different nave, dSPM just scales by a factor sqrt(nave)
stcs = apply_inverse_epochs(epochs, inverse_operator, lambda2, method, label,
pick_ori="normal", nave=evoked.nave)
# Mean across trials but not across vertices in label
mean_stc = sum(stcs) / len(stcs)
# compute sign flip to avoid signal cancellation when averaging signed values
flip = mne.label_sign_flip(label, inverse_operator['src'])
label_mean = np.mean(mean_stc.data, axis=0)
label_mean_flip = np.mean(flip[:, np.newaxis] * mean_stc.data, axis=0)
# Get inverse solution by inverting evoked data
stc_evoked = apply_inverse(evoked, inverse_operator, lambda2, method,
pick_ori="normal")
# apply_inverse() does whole brain, so sub-select label of interest
stc_evoked_label = stc_evoked.in_label(label)
# Average over label (not caring to align polarities here)
label_mean_evoked = np.mean(stc_evoked_label.data, axis=0)
```

Out:

```
Reading inverse operator decomposition from /home/circleci/mne_data/MNE-sample-data/MEG/sample/sample_audvis-meg-oct-6-meg-inv.fif...
Reading inverse operator info...
[done]
Reading inverse operator decomposition...
[done]
305 x 305 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
Noise covariance matrix read.
22494 x 22494 diagonal covariance (kind = 2) found.
Source covariance matrix read.
22494 x 22494 diagonal covariance (kind = 6) found.
Orientation priors read.
22494 x 22494 diagonal covariance (kind = 5) found.
Depth priors read.
Did not find the desired covariance matrix (kind = 3)
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
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
Source spaces transformed to the inverse solution coordinate frame
Opening raw data file /home/circleci/mne_data/MNE-sample-data/MEG/sample/sample_audvis_filt-0-40_raw.fif...
Read a total of 4 projection items:
PCA-v1 (1 x 102) idle
PCA-v2 (1 x 102) idle
PCA-v3 (1 x 102) idle
Average EEG reference (1 x 60) idle
Range : 6450 ... 48149 = 42.956 ... 320.665 secs
Ready.
Not setting metadata
Not setting metadata
72 matching events found
Setting baseline interval to [-0.19979521315838786, 0.0] sec
Applying baseline correction (mode: mean)
Created an SSP operator (subspace dimension = 3)
4 projection items activated
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on MAG : ['MEG 1711']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Removing projector <Projection | Average EEG reference, active : True, n_channels : 60>
Preparing the inverse operator for use...
Scaled noise and source covariance from nave = 1 to nave = 55
Created the regularized inverter
Created an SSP operator (subspace dimension = 3)
Created the whitener using a noise covariance matrix with rank 302 (3 small eigenvalues omitted)
Computing noise-normalization factors (dSPM)...
[done]
Picked 305 channels from the data
Computing inverse...
Eigenleads need to be weighted ...
Processing epoch : 1 / 72 (at most)
Processing epoch : 2 / 72 (at most)
Processing epoch : 3 / 72 (at most)
Processing epoch : 4 / 72 (at most)
Processing epoch : 5 / 72 (at most)
Processing epoch : 6 / 72 (at most)
Processing epoch : 7 / 72 (at most)
Processing epoch : 8 / 72 (at most)
Processing epoch : 9 / 72 (at most)
Processing epoch : 10 / 72 (at most)
Rejecting epoch based on EOG : ['EOG 061']
Processing epoch : 11 / 72 (at most)
Processing epoch : 12 / 72 (at most)
Processing epoch : 13 / 72 (at most)
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Processing epoch : 14 / 72 (at most)
Processing epoch : 15 / 72 (at most)
Processing epoch : 16 / 72 (at most)
Processing epoch : 17 / 72 (at most)
Rejecting epoch based on EOG : ['EOG 061']
Processing epoch : 18 / 72 (at most)
Processing epoch : 19 / 72 (at most)
Processing epoch : 20 / 72 (at most)
Rejecting epoch based on EOG : ['EOG 061']
Processing epoch : 21 / 72 (at most)
Processing epoch : 22 / 72 (at most)
Processing epoch : 23 / 72 (at most)
Rejecting epoch based on MAG : ['MEG 1711']
Processing epoch : 24 / 72 (at most)
Processing epoch : 25 / 72 (at most)
Processing epoch : 26 / 72 (at most)
Processing epoch : 27 / 72 (at most)
Processing epoch : 28 / 72 (at most)
Rejecting epoch based on EOG : ['EOG 061']
Processing epoch : 29 / 72 (at most)
Processing epoch : 30 / 72 (at most)
Processing epoch : 31 / 72 (at most)
Rejecting epoch based on EOG : ['EOG 061']
Processing epoch : 32 / 72 (at most)
Processing epoch : 33 / 72 (at most)
Rejecting epoch based on EOG : ['EOG 061']
Processing epoch : 34 / 72 (at most)
Processing epoch : 35 / 72 (at most)
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Processing epoch : 36 / 72 (at most)
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Processing epoch : 37 / 72 (at most)
Processing epoch : 38 / 72 (at most)
Processing epoch : 39 / 72 (at most)
Processing epoch : 40 / 72 (at most)
Processing epoch : 41 / 72 (at most)
Processing epoch : 42 / 72 (at most)
Processing epoch : 43 / 72 (at most)
Processing epoch : 44 / 72 (at most)
Rejecting epoch based on EOG : ['EOG 061']
Processing epoch : 45 / 72 (at most)
Rejecting epoch based on EOG : ['EOG 061']
Processing epoch : 46 / 72 (at most)
Processing epoch : 47 / 72 (at most)
Processing epoch : 48 / 72 (at most)
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Processing epoch : 49 / 72 (at most)
Processing epoch : 50 / 72 (at most)
Processing epoch : 51 / 72 (at most)
Processing epoch : 52 / 72 (at most)
Processing epoch : 53 / 72 (at most)
Processing epoch : 54 / 72 (at most)
Processing epoch : 55 / 72 (at most)
[done]
Preparing the inverse operator for use...
Scaled noise and source covariance from nave = 1 to nave = 55
Created the regularized inverter
Created an SSP operator (subspace dimension = 3)
Created the whitener using a noise covariance matrix with rank 302 (3 small eigenvalues omitted)
Computing noise-normalization factors (dSPM)...
[done]
Applying inverse operator to "1"...
Picked 305 channels from the data
Computing inverse...
Eigenleads need to be weighted ...
Computing residual...
Explained 59.3% variance
dSPM...
[done]
```

View activation time-series to illustrate the benefit of aligning/flipping

```
times = 1e3 * stcs[0].times # times in ms
plt.figure()
h0 = plt.plot(times, mean_stc.data.T, 'k')
h1, = plt.plot(times, label_mean, 'r', linewidth=3)
h2, = plt.plot(times, label_mean_flip, 'g', linewidth=3)
plt.legend((h0[0], h1, h2), ('all dipoles in label', 'mean',
'mean with sign flip'))
plt.xlabel('time (ms)')
plt.ylabel('dSPM value')
plt.show()
```

Viewing single trial dSPM and average dSPM for unflipped pooling over label Compare to (1) Inverse (dSPM) then average, (2) Evoked then dSPM

```
# Single trial
plt.figure()
for k, stc_trial in enumerate(stcs):
plt.plot(times, np.mean(stc_trial.data, axis=0).T, 'k--',
label='Single Trials' if k == 0 else '_nolegend_',
alpha=0.5)
# Single trial inverse then average.. making linewidth large to not be masked
plt.plot(times, label_mean, 'b', linewidth=6,
label='dSPM first, then average')
# Evoked and then inverse
plt.plot(times, label_mean_evoked, 'r', linewidth=2,
label='Average first, then dSPM')
plt.xlabel('time (ms)')
plt.ylabel('dSPM value')
plt.legend()
plt.show()
```

**Total running time of the script:** ( 0 minutes 7.610 seconds)

**Estimated memory usage:** 61 MB