mne.inverse_sparse.mixed_norm(evoked, forward, noise_cov, alpha, 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, 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.

evokedinstance of Evoked or list of instances of Evoked

Evoked data to invert.


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 | ‘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, 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). This is effectively ignored when method='eLORETA'.

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


Maximum number of iterations.


Tolerance parameter.

active_set_sizeint | None

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


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).


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.


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


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


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 | 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.

pick_oriNone | “normal” | “vector”


  • 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.

verbosebool, str, int, or None

If not None, override default verbose level (see mne.verbose() and Logging documentation for more). If used, it should be passed as a keyword-argument only.

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




A. Gramfort, M. Kowalski, M. Hämäläinen, “Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods”, Physics in Medicine and Biology, 2012.


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.