Article

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

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

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.

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• "Prior information about the current dipole distribution has been used in the MEG/EEG inverse problem literature in order to obtain unique estimates. This information has taken the form of a probabilistic model or optimization penalty that implicitly or explicitly assumes cortical activity is either independent across time [2]–[5], temporally or spatio-temporally smooth [6]–[10], or follow a linear dynamic process [11]– [13]. While these priors alleviate issues related to the nonuniqueness of source estimates, they do not necessarily improve on the limitations that stem from the rank deficiency and restricted sensitivity of the lead field matrix. "
##### Article: An Analysis of How Spatiotemporal Dynamic Models of Brain Activity Could Improve MEG/EEG Inverse Solutions
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ABSTRACT: MEG and EEG are noninvasive functional neuroimaging techniques that provide recordings of brain activity with high temporal resolution, and thus provide a unique window to study fast time-scale neural dynamics in humans. However, the accuracy of brain activity estimates resulting from these data is limited mainly because 1) the number of sensors is much smaller than the number of sources, and 2) the low sensitivity of the recording device to deep or radially oriented sources. These factors limit the number of sources that can be recovered and bias estimates to superficial cortical areas, resulting in the need to include a priori information about the source activity. The question of how to specify this information and how it might lead to improved solutions remains a critical open problem. In this paper we show that the incorporation of knowledge about the brain's underlying connectivity and spatiotemporal dynamics could dramatically improve inverse solutions. To do this, we develop the concept of the \textit{dynamic lead field mapping}, which expresses how information about source activity at a given time is mapped not only to the immediate measurement, but to a time series of measurements. With this mapping we show that the number of source parameters that can be recovered could increase by up to a factor of ${\sim20}$, and that such improvement is primarily represented by deep cortical areas. Our result implies that future developments in MEG/EEG analysis that model spatialtemporal dynamics have the potential to dramatically increase source resolution.
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• "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. "
##### Article: MEG/EEG source imaging with a non-convex penalty in the time-frequency domain

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• "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. "