Time-Frequency Mixed-Norm Estimates: Sparse M/EEG imaging with non-stationary source activations

INRIA, Parietal team, Saclay, France
NeuroImage (Impact Factor: 6.36). 01/2013; 70. DOI: 10.1016/j.neuroimage.2012.12.051
Source: PubMed


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.

49 Reads
  • Source
    • "Moreover, the BCD scheme is memory-efficient. Extending irTF-MxNE to source reconstruction with a loose orientation constraint or free orientation is not presented here but is straightforward using an additional weighted 2 -norm over orientations [5]. The first iteration of the proposed irTF-MxNE approach is equivalent to computing a standard TF-MxNE solution. "
  • Source
    • "Regarding the dictionary-based sparse techniques, the most famous is MCE (Minimum Current Estimate) [5], which computes minimum ℓ 1 -norm estimates. Note that cosparse approaches were recently proposed applying for instance a discrete Gabor transform [8] as analysis operator [9] to the current source activi- ties. "
  • Source
    • "Nevertheless, assessment of brain activity reconstruction, and in turn, evaluation of connectivity networks in most of the cases is limited by the implicit assumption about spatial and temporal stationarity throughout the entire measurement interval [8]. This assumption is far from being totally realistic in many practical scenarios, where brain activity has strong non-stationary spatio-temporal dynamics [9], [8]. This work assumes that the brain activity can be represented by a set of small spatial basis functions or patches enforcing compact and sparse support. "
    [Show abstract] [Hide abstract]
    ABSTRACT: Electroencephalographic (EEG) data give a direct non-invasive measurement of neural brain activity. Nevertheless, the common assumption about EEG stationarity (time-invariant process) is a strong limitation for understanding real behavior of underlying neural networks. Here, we propose an approach for finding networks of brain regions connected by functional associations (functional connectivity) that vary along the time. To this end, we compute a set of a priori spatial dictionaries that represent brain areas with similar temporal stochastic dynamics, and then, we model relationship between areas as a time-varying process. We test our approach in both simulated and real EEG data where results show that inherent interpretability provided by the time-varying process can be useful to describe underlying neural networks.
Show more