Source localization with a custom inverse solver¶
The objective of this example is to show how to plug a custom inverse solver in MNE in order to facilate empirical comparison with the methods MNE already implements (wMNE, dSPM, sLORETA, eLORETA, LCMV, DICS, (TF-)MxNE etc.).
This script is educational and shall be used for methods evaluations and new developments. It is not meant to be an example of good practice to analyse your data.
The example makes use of 2 functions
so changes can be limited to the
solver function (which only takes three
parameters: the whitened data, the gain matrix and the number of orientations)
in order to try out another inverse algorithm.
import numpy as np from scipy import linalg import mne from mne.datasets import sample 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' condition = 'Left Auditory' # Read noise covariance matrix noise_cov = mne.read_cov(cov_fname) # Handling average file evoked = mne.read_evokeds(ave_fname, condition=condition, baseline=(None, 0)) evoked.crop(tmin=0.04, tmax=0.18) evoked = evoked.pick_types(eeg=False, meg=True) # Handling forward solution forward = mne.read_forward_solution(fwd_fname)
365 x 365 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 59) active Reading /home/circleci/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 Auditory) 0 CTF compensation matrices available nave = 55 - aspect type = 100 Projections have already been applied. Setting proj attribute to True. Applying baseline correction (mode: mean) Removing projector <Projection | Average EEG reference, active : True, n_channels : 60> Reading forward solution from /home/circleci/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
Auxiliary function to run the solver
def apply_solver(solver, evoked, forward, noise_cov, loose=0.2, depth=0.8): """Call a custom solver on evoked data. This function does all the necessary computation: - to select the channels in the forward given the available ones in the data - to take into account the noise covariance and do the spatial whitening - to apply loose orientation constraint as MNE solvers - to apply a weigthing of the columns of the forward operator as in the weighted Minimum Norm formulation in order to limit the problem of depth bias. Parameters ---------- solver : callable The solver takes 3 parameters: data M, gain matrix G, number of dipoles orientations per location (1 or 3). A solver shall return 2 variables: X which contains the time series of the active dipoles and an active set which is a boolean mask to specify what dipoles are present in X. evoked : instance of mne.Evoked The evoked data forward : instance of Forward The forward solution. noise_cov : instance of Covariance The noise covariance. loose : float in [0, 1] | 'auto' Value that weights the source variances of the dipole components that are parallel (tangential) to the cortical surface. If loose is 0 then the solution is computed with fixed orientation. If loose is 1, it corresponds to free orientations. The default value ('auto') is set to 0.2 for surface-oriented source space and set to 1.0 for volumic or discrete source space. depth : None | float in [0, 1] Depth weighting coefficients. If None, no depth weighting is performed. Returns ------- stc : instance of SourceEstimate The source estimates. """ # Import the necessary private functions from mne.inverse_sparse.mxne_inverse import \ (_prepare_gain, is_fixed_orient, _reapply_source_weighting, _make_sparse_stc) all_ch_names = evoked.ch_names # Handle depth weighting and whitening (here is no weights) forward, gain, gain_info, whitener, source_weighting, mask = _prepare_gain( forward, evoked.info, noise_cov, pca=False, depth=depth, loose=loose, weights=None, weights_min=None, rank=None) # Select channels of interest sel = [all_ch_names.index(name) for name in gain_info['ch_names']] M = evoked.data[sel] # Whiten data M = np.dot(whitener, M) n_orient = 1 if is_fixed_orient(forward) else 3 X, active_set = solver(M, gain, n_orient) X = _reapply_source_weighting(X, source_weighting, active_set) stc = _make_sparse_stc(X, active_set, forward, tmin=evoked.times, tstep=1. / evoked.info['sfreq']) return stc
Define your solver
def solver(M, G, n_orient): """Run L2 penalized regression and keep 10 strongest locations. Parameters ---------- M : array, shape (n_channels, n_times) The whitened data. G : array, shape (n_channels, n_dipoles) The gain matrix a.k.a. the forward operator. The number of locations is n_dipoles / n_orient. n_orient will be 1 for a fixed orientation constraint or 3 when using a free orientation model. n_orient : int Can be 1 or 3 depending if one works with fixed or free orientations. If n_orient is 3, then ``G[:, 2::3]`` corresponds to the dipoles that are normal to the cortex. Returns ------- X : array, (n_active_dipoles, n_times) The time series of the dipoles in the active set. active_set : array (n_dipoles) Array of bool. Entry j is True if dipole j is in the active set. We have ``X_full[active_set] == X`` where X_full is the full X matrix such that ``M = G X_full``. """ inner = np.dot(G, G.T) trace = np.trace(inner) K = linalg.solve(inner + 4e-6 * trace * np.eye(G.shape), G).T K /= np.linalg.norm(K, axis=1)[:, None] X = np.dot(K, M) indices = np.argsort(np.sum(X ** 2, axis=1))[-10:] active_set = np.zeros(G.shape, dtype=bool) for idx in indices: idx -= idx % n_orient active_set[idx:idx + n_orient] = True X = X[active_set] return X, active_set
Apply your custom solver
info["bads"] and noise_cov["bads"] do not match, excluding bad channels from both Computing inverse operator with 305 channels. 305 out of 366 channels remain after picking Selected 305 channels Whitening the forward solution. Created an SSP operator (subspace dimension = 3) Computing rank from covariance with rank=None Using tolerance 3.5e-13 (2.2e-16 eps * 305 dim * 5.2 max singular value) Estimated rank (mag + grad): 302 MEG: rank 302 computed from 305 data channels with 3 projectors Setting small MEG eigenvalues to zero (without PCA) Creating the source covariance matrix Adjusting source covariance matrix. combining the current components...
View in 2D and 3D (“glass” brain like 3D plot)
Total number of active sources: 10
Total running time of the script: ( 0 minutes 4.262 seconds)
Estimated memory usage: 104 MB