Time-frequency mixed-norm estimates: Sparse M/EEG imaging with non-stationary source activations

Abstract

Magnetoencephalography (MEG) and electroencephalography (EEG) allow functional brain imaging with high temporal resolution. While solving the inverse problem independently at every time point can give an image of the active brain at every millisecond, such a procedure does not capitalize on the temporal dynamics of the signal. Linear inverse methods (Minimum-norm, dSPM, sLORETA, beamformers) typically assume that the signal is stationary: regularization parameter and data covariance are independent of time and the time varying signal-to-noise ratio (SNR). Other recently proposed non-linear inverse solvers promoting focal activations estimate the sources in both space and time while also assuming stationary sources during a time interval. However such an hypothesis only holds for short time intervals. To overcome this limitation, we propose time-frequency mixed-norm estimates (TF-MxNE), which use time-frequency analysis to regularize the ill-posed inverse problem. This method makes use of structured sparse priors defined in the time-frequency domain, offering more accurate estimates by capturing the non-stationary and transient nature of brain signals. State-of-the-art convex optimization procedures based on proximal operators are employed, allowing the derivation of a fast estimation algorithm. The accuracy of the TF-MxNE is compared to recently proposed inverse solvers with help of simulations and by analyzing publicly available MEG datasets.

Contrasting functional imaging parametric maps: The mislocation problem and alternative solutions

“…Even larger mislocation errors would be foreseeably obtained for maps reconstructed from electroencephalographic (EEG) signals since they spread more than MEG signals and their propagation is harder to model (H€ am€ al€ ainen et al, 1993). One way to avoid the extreme smoothness of MEG maps is to use spatially sparse imaging methods such as, e.g., minimum current estimation (Uutela et al, 1999), minimum mixed-norm estimation (Gramfort et al, 2013(Gramfort et al, , 2012, or the multiple sparse priors approach (Friston et al, 2008). In this case the MEG maps are very focal, but this opposite extreme poses other problems to contrast two different conditions at the group level (unless maps are smoothed afterwards).…”

Spatio-temporal reconstruction of brain dynamics from EEG with a Markov prior

“…Although no gold standard EEG inverse solver has been established, the field is con-20 verging on methods that employ spatial sparsity (Gorodnitsky and Rao, 1997;Wipf and Rao, 2007;Vega-Hernández et al, 2008;Friston et al, 2008;Zhang and Rao, 2011;Stahlhut et al, 2011;Montoya-Martinez et al, 2012;Gramfort et al, 2013;Hansen et al, 2013c;Hansen and Hansen, 2014;Andersen et al, 2014). Evidence was presented, in recent work (Delorme et al, 2012) that the instantaneous independent components of EEG 25 signals are dipolar and localized.…”

“…While useful for short time windows, this may be less appropriate for more extended and non-stationary settings. Recently proposed methods enforce temporal coherency while also allowing for dynamic activation patterns (Montoya-Martinez et al, 2012;Gramfort et al, 2013). These methods model 55 the temporal dynamics more realistically by assuming brain areas to be sequentially or simultaneously activated during, e.g.…”

“…These methods model 55 the temporal dynamics more realistically by assuming brain areas to be sequentially or simultaneously activated during, e.g. a stimulus after which the activity returns to a baseline level (Gramfort et al, 2013). Both methods employ a mixed-norm scheme to recover what is hypothesized to be a structured sparsity pattern across time, see also (Haufe et al, 2008;Gramfort et al, 2012).…”

“…In line with previous EEG simulation studies (Friston et al, 2008;Stahlhut et al, 2011;Montoya-Martinez et al, 2012;Gramfort et al, 2013) we generated synthetic EEG signals by randomly planting one to four sources and projecting their temporal dynamics through a forward model. The sources were modeled as having a spatial distribution given by the earlier described basis EEG electrodes through a forward model generated for subject "A" in the real data experiment described below.…”