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.
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ABSTRACT: Network theory and inverse modeling are two standard tools of applied physics, whose combination is needed when studying the dynamical organization of spatially distributed systems from indirect measurements. However, the associated connectivity estimation may be affected by spatial leakage, an artifact of inverse modeling that limits the interpretability of network analysis. This paper investigates general analytical aspects pertaining to this issue. First, the existence of spatial leakage is derived from the topological structure of inverse operators. Then, the geometry of spatial leakage is modeled and used to define a geometric correction scheme, which limits spatial leakage effects in connectivity estimation. Finally, this new approach for network analysis is compared analytically to existing methods based on linear regressions, which are shown to yield biased coupling estimates.Physical Review E 01/2015; 91(01). DOI:10.1103/PhysRevE.91.012823 · 2.33 Impact Factor
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ABSTRACT: Multimodal data is ubiquitous in engineering, communication, robotics, vision or more generally speaking in industry and the sciences. All disciplines have developed their respective sets of analytic tools to fuse the information that is available in all measured modalities. In this paper we provide a review of classical as well as recent machine learning methods (specifically factor models) for fusing information from functional neuroimaging techniques such as LFP, EEG, MEG, fNIRS and fMRI. Early and late fusion scenarios are distinguished and appropriate factor models for the respective scenarios are presented along with example applications from selected multimodal neuroimaging studies. Further emphasis is given to the interpretability of the resulting model parameters, in particular by highlighting how factor models relate to physical models needed for source localization. The methods we discuss allow to extract information from neural data, which ultimately contributes to (a) better neuroscientific understanding, (b) enhance diagnostic performance and (c) discover neural signals of interest that correlate maximally with a given cognitive paradigm. While we clearly study the multimodal functional neuroimaging challenge, the discussed machine learning techniques have a wide applicability beyond, i.e. in general data fusion and may thus be informative to the general interested reader.
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ABSTRACT: Knowing how the Human brain is anatomically and functionally organized at the level of a group of healthy individuals or patients is the primary goal of neuroimaging research. Yet computing an average of brain imaging data defined over a voxel grid or a triangulation remains a challenge. Data are large, the geometry of the brain is complex and the between subjects variability leads to spatially or temporally non-overlapping effects of interest. To address the problem of variability, data are commonly smoothed before group linear averaging. In this work we build on ideas originally introduced by Kantorovich to propose a new algorithm that can average efficiently non-normalized data defined over arbitrary discrete domains using transportation metrics. We show how Kantorovich means can be linked to Wasserstein barycenters in order to take advantage of an entropic smoothing approach. It leads to a smooth convex optimization problem and an algorithm with strong convergence guarantees. We illustrate the versatility of this tool and its empirical behavior on functional neuroimaging data, functional MRI and magnetoencephalography (MEG) source estimates, defined on voxel grids and triangulations of the folded cortical surface.