mne.inverse_sparse.tf_mixed_norm(evoked, forward, noise_cov, loose='auto', depth=0.8, maxit=3000, tol=0.0001, weights=None, weights_min=0.0, pca=True, debias=True, wsize=64, tstep=4, window=0.02, return_residual=False, return_as_dipoles=False, alpha=None, l1_ratio=None, dgap_freq=10, rank=None, pick_ori=None, n_tfmxne_iter=1, verbose=None)[source]

Time-Frequency Mixed-norm estimate (TF-MxNE).

Compute L1/L2 + L1 mixed-norm solution on time-frequency dictionary. Works with evoked data 12.

evokedinstance of Evoked

Evoked data to invert.


Forward operator.

noise_covinstance of Covariance

Noise covariance to compute whitener.

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.

weightsNone | array | SourceEstimate

Weight for penalty in mixed_norm. Can be None or 1d array of length n_sources or a SourceEstimate e.g. obtained with wMNE or dSPM or fMRI.


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


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


Remove coefficient amplitude bias due to L1 penalty.

wsizeint or array_like

Length of the STFT window in samples (must be a multiple of 4). If an array is passed, multiple TF dictionaries are used (each having its own wsize and tstep) and each entry of wsize must be a multiple of 4. See 3.

tstepint or array_like

Step between successive windows in samples (must be a multiple of 2, a divider of wsize and smaller than wsize/2) (default: wsize/2). If an array is passed, multiple TF dictionaries are used (each having its own wsize and tstep), and each entry of tstep must be a multiple of 2 and divide the corresponding entry of wsize. See 3.

windowfloat or (float, float)

Length of time window used to take care of edge artifacts in seconds. It can be one float or float if the values are different for left and right window length.


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


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

alphafloat in [0, 100) or None

Overall regularization parameter. If alpha and l1_ratio are not None, alpha_space and alpha_time are overridden by alpha * alpha_max * (1. - l1_ratio) and alpha * alpha_max * l1_ratio. 0 means no regularization, 100 would give 0 active dipole.

l1_ratiofloat in [0, 1] or None

Proportion of temporal regularization. If l1_ratio and alpha are not None, alpha_space and alpha_time are overridden by alpha * alpha_max * (1. - l1_ratio) and alpha * alpha_max * l1_ratio. 0 means no time regularization a.k.a. MxNE.

dgap_freqint or numpy.inf

The duality gap is evaluated every dgap_freq iterations.

rankNone | ‘info’ | ‘full’ | dict

This controls the rank computation that can be read from the measurement info or estimated from the data.


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


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.


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.


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”


  • 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.


Number of TF-MxNE iterations. If > 1, iterative reweighting is applied.

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.

stcinstance of SourceEstimate

Source time courses.

residualinstance of Evoked

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

See also




Alexandre Gramfort, Daniel T. Strohmeier, Jens Haueisen, Matti S. Hämäläinen, and Matthieu Kowalski. Time-frequency mixed-norm estimates: sparse M/EEG imaging with non-stationary source activations. NeuroImage, 70:410–422, 2013. doi:10.1016/j.neuroimage.2012.12.051.


Alexandre Gramfort, Daniel Strohmeier, Jens Haueisen, Matti S. Hämäläinen, and Matthieu Kowalski. Functional brain imaging with M/EEG using structured sparsity in time-frequency dictionaries. In Gábor Székely and Horst K. Hahn, editors, Information Processing in Medical Imaging, volume 6801, pages 600–611. Springer, Berlin; Heidelberg, 2011. doi:10.1007/978-3-642-22092-0_49.


Yousra Bekhti, Daniel Strohmeiery, Mainak Jas, Roland Badeau, and Alexandre Gramfort. M/EEG source localization with multi-scale time-frequency dictionaries. In Proceedings of PRNI-2016, 1–4. Trento, 2016. IEEE. doi:10.1109/PRNI.2016.7552337.