mne.inverse_sparse.mixed_norm

mne.inverse_sparse.mixed_norm(evoked, forward, noise_cov, alpha='sure', loose='auto', depth=0.8, maxit=3000, tol=0.0001, active_set_size=10, debias=True, time_pca=True, weights=None, weights_min=0.0, solver='auto', n_mxne_iter=1, return_residual=False, return_as_dipoles=False, dgap_freq=10, rank=None, pick_ori=None, sure_alpha_grid='auto', random_state=None, verbose=None)

Mixed-norm estimate (MxNE) and iterative reweighted MxNE (irMxNE).

Compute L1/L2 mixed-norm solution 1 or L0.5/L2 2 mixed-norm solution on evoked data.

Parameters

evokedinstance of Evoked or list of instances of Evoked

Evoked data to invert.

forwarddict

Forward operator.

noise_covinstance of Covariance

Noise covariance to compute whitener.

alphafloat | str

Regularization parameter. If float it should be in the range [0, 100): 0 means no regularization, 100 would give 0 active dipole. If 'sure' (default), the SURE method from 3 will be used.

Changed in version 0.24: The default was changed to 'sure'.

loosefloat | ‘auto’ | dict

Value that weights the source variances of the dipole components that are parallel (tangential) to the cortical surface. Can be:

• float between 0 and 1 (inclusive)

  If 0, then the solution is computed with fixed orientation. If 1, it corresponds to free orientations.

• 'auto' (default)

  Uses 0.2 for surface source spaces (unless fixed is True) and 1.0 for other source spaces (volume or mixed).

• dict

  Mapping from the key for a given source space type (surface, volume, discrete) to the loose value. Useful mostly for mixed source spaces.

depthNone | float | dict

How to weight (or normalize) the forward using a depth prior. If float (default 0.8), it acts as the depth weighting exponent (exp) to use None is equivalent to 0, meaning no depth weighting is performed. It can also be a dict containing keyword arguments to pass to mne.forward.compute_depth_prior() (see docstring for details and defaults). This is effectively ignored when method='eLORETA'.

Changed in version 0.20: Depth bias ignored for method='eLORETA'.

maxitint

Maximum number of iterations.

tolfloat

Tolerance parameter.

active_set_sizeint | None

Size of active set increment. If None, no active set strategy is used.

debiasbool

Remove coefficient amplitude bias due to L1 penalty.

time_pcabool or int

If True the rank of the concatenated epochs is reduced to its true dimension. If is ‘int’ the rank is limited to this value.

weightsNone | array | SourceEstimate

Weight for penalty in mixed_norm. Can be None, a 1d array with shape (n_sources,), or a SourceEstimate (e.g. obtained with wMNE, dSPM, or fMRI).

weights_minfloat

Do not consider in the estimation sources for which weights is less than weights_min.

solver‘cd’ | ‘bcd’ | ‘auto’

The algorithm to use for the optimization. ‘cd’ uses coordinate descent, and ‘bcd’ applies block coordinate descent. ‘cd’ is only available for fixed orientation.

n_mxne_iterint

The number of MxNE iterations. If > 1, iterative reweighting is applied.

return_residualbool

If True, the residual is returned as an Evoked instance.

return_as_dipolesbool

If True, the sources are returned as a list of Dipole instances.

dgap_freqint or numpy.inf

The duality gap is evaluated every dgap_freq iterations. Ignored if solver is ‘cd’.

rankNone | ‘info’ | ‘full’ | dict

This controls the rank computation that can be read from the measurement info or estimated from the data. When a noise covariance is used for whitening, this should reflect the rank of that covariance, otherwise amplification of noise components can occur in whitening (e.g., often during source localization).

None

The rank will be estimated from the data after proper scaling of different channel types.

'info'

The rank is inferred from info. If data have been processed with Maxwell filtering, the Maxwell filtering header is used. Otherwise, the channel counts themselves are used. In both cases, the number of projectors is subtracted from the (effective) number of channels in the data. For example, if Maxwell filtering reduces the rank to 68, with two projectors the returned value will be 66.

'full'

The rank is assumed to be full, i.e. equal to the number of good channels. If a Covariance is passed, this can make sense if it has been (possibly improperly) regularized without taking into account the true data rank.

dict

Calculate the rank only for a subset of channel types, and explicitly specify the rank for the remaining channel types. This can be extremely useful if you already know the rank of (part of) your data, for instance in case you have calculated it earlier.

This parameter must be a dictionary whose keys correspond to channel types in the data (e.g. 'meg', 'mag', 'grad', 'eeg'), and whose values are integers representing the respective ranks. For example, {'mag': 90, 'eeg': 45} will assume a rank of 90 and 45 for magnetometer data and EEG data, respectively.

The ranks for all channel types present in the data, but not specified in the dictionary will be estimated empirically. That is, if you passed a dataset containing magnetometer, gradiometer, and EEG data together with the dictionary from the previous example, only the gradiometer rank would be determined, while the specified magnetometer and EEG ranks would be taken for granted.

The default is None.

New in version 0.18.

pick_oriNone | “normal” | “vector”

Options:

• None

  Pooling is performed by taking the norm of loose/free orientations. In case of a fixed source space no norm is computed leading to signed source activity.

• "normal"

  Only the normal to the cortical surface is kept. This is only implemented when working with loose orientations.

• "vector"

  No pooling of the orientations is done, and the vector result will be returned in the form of a mne.VectorSourceEstimate object.

sure_alpha_gridarray | str

If 'auto' (default), the SURE is evaluated along 15 uniformly distributed alphas between alpha_max and 0.1 * alpha_max. If array, the grid is directly specified. Ignored if alpha is not “sure”.

New in version 0.24.

random_stateint | None

The random state used in a random number generator for delta and epsilon used for the SURE computation. Defaults to None.

New in version 0.24.

verbosebool | str | int | None

Control verbosity of the logging output. If None, use the default verbosity level. See the logging documentation and mne.verbose() for details. Should only be passed as a keyword argument.

Returns

stcSourceEstimate | list of SourceEstimate

Source time courses for each evoked data passed as input.

residualinstance of Evoked

The residual a.k.a. data not explained by the sources. Only returned if return_residual is True.

See also

tf_mixed_norm

References

1

Alexandre Gramfort, Matthieu Kowalski, and Matti S. Hämäläinen. Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods. Physics in Medicine and Biology, 57(7):1937–1961, 2012. doi:10.1088/0031-9155/57/7/1937.

2

Daniel Strohmeier, Yousra Bekhti, Jens Haueisen, and Alexandre Gramfort. The iterative reweighted mixed-norm estimate for spatio-temporal MEG/EEG source reconstruction. IEEE Transactions on Medical Imaging, 35(10):2218–2228, 2016. doi:10.1109/TMI.2016.2553445.

3

Charles-Alban Deledalle, Samuel Vaiter, Jalal Fadili, and Gabriel Peyré. Stein unbiased gradient estimator of the risk (sugar) for multiple parameter selection. SIAM Journal on Imaging Sciences, 7(4):2448–2487, 2014. URL: https://doi.org/10.1137/140968045, doi:10.1137/140968045.

Examples using mne.inverse_sparse.mixed_norm

The SourceEstimate data structure

The SourceEstimate data structure

Compute sparse inverse solution with mixed norm: MxNE and irMxNE

Compute sparse inverse solution with mixed norm: MxNE and irMxNE

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