# mne.inverse_sparse.mixed_norm¶

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

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 in range [0, 100)

Regularization parameter. 0 means no regularization, 100 would give 0 active dipole.

loosefloat 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

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, which must be between 0 and 1. 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).

maxitint

Maximum number of iterations.

tolfloat

Tolerance parameter.

active_set_size

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

pcabool

If True the rank of the data is reduced to true dimension.

debiasbool

Remove coefficient amplitude bias due to L1 penalty.

time_pca

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

weights

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‘prox’ | ‘cd’ | ‘bcd’ | ‘auto’

The algorithm to use for the optimization. ‘prox’ stands for proximal iterations using the FISTA algorithm, ‘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_freq

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

rankNone | dict | ‘info’ | ‘full’

This controls the rank computation that can be read from the measurement info or estimated from the data. See Notes of mne.compute_rank() for details.The default is None.

New in version 0.18.

verbose

If not None, override default verbose level (see mne.verbose() and Logging documentation for more).

Returns
stc

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.

References

1

A. Gramfort, M. Kowalski, M. Hamalainen, “Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods”, Physics in Medicine and Biology, 2012. https://doi.org/10.1088/0031-9155/57/7/1937

2

D. Strohmeier, Y. Bekhti, J. Haueisen, A. Gramfort, “The Iterative Reweighted Mixed-Norm Estimate for Spatio-Temporal MEG/EEG Source Reconstruction”, IEEE Transactions of Medical Imaging, Volume 35 (10), pp. 2218-2228, 2016.