Sofie Therese Hansen

Data-driven forward model inference for EEG brain imaging.

Electroencephalography (EEG) is a flexible and accessible tool with excellent temporal resolution but with a spatial resolution hampered by volume conduction. Reconstruction of the cortical sources of measured EEG activity partly alleviates this problem and effectively turns EEG into a brain imaging device. The quality of the source reconstruction depends on the forward model which details head geometry and conductivities of different head compartments. These person-specific factors are complex to determine, requiring detailed knowledge of the subjects anatomy and physiology. In this proof-of-concept study, we show that, even when anatomical knowledge is unavailable, a suitable forward model can be estimated directly from the EEG. We propose a data-driven approach that provides a low-dimensional parametrization of head geometry and compartment conductivities, built using a corpus of forward models. Combined with only a recorded EEG signal, we are able to estimate both the brain sources and a person-specific forward model by optimizing this parametrization. We thus not only solve an inverse problem, but also optimize over its specification. Our work demonstrates that personalized EEG brain imaging is possible, even when the head geometry and conductivities are unknown.

Expansion of the Variational Garrote to a Multiple Measurement Vectors Model

(08/12/2018) Expansion of the Variational Garrote to a Multiple Measurement Vectors Model The recovery of sparse signals in underdetermined systems is the focus of this paper. We propose an expanded version of the Variational Garrote, originally presented by Kappen (2011), which can use multiple measurement vectors (MMVs) to further improve source retrieval performance. We show its superiority compared to the original formulation and demonstrate its ability to correctly estimate both the sources’ location and their magnitude. Finally evidence is given of the high performance of the proposed algorithm compared to other MMV models.

EEG source reconstruction performance as a function of skull conductance contrast

Through simulated EEG we investigate the effect of the forward models applied skull:scalp conductivity ratio on the source reconstruction performance. We show that having a higher conductivity ratio generally leads to improvement of the solution. Additionally we see a clear connection between higher conductivity ratios and lower coherence, thus a reduction of the ill-posedness of the EEG inverse problem. Finally we show on real EEG data the stability of the strongest source recovered across conductivity ratios.

Learning the solution sparsity of an ill-posed linear inverse problem with the Variational Garrote

The Variational Garrote is a promising new approach for sparse solutions of ill-posed linear inverse problems (Kappen and Gomez, 2012). We reformulate the prior of the Variational Garrote to follow a simple Binomial law and assign a Beta hyper-prior on the parameter. With the new prior the Variational Garrote, we show, has a wide range of parameter values for which it at the same time provides low test error and high retrieval of the true feature locations. Furthermore, the new form of the prior and associated hyper-prior leads to a simple update rule in a Bayesian variational inference scheme for its hyperparameter. As a second contribution we provide evidence that the new procedure can improve on cross-validation of the parameters and we find that the new formulation of the prior outperforms the original formulation when both are cross-validated to determine hyperparameters.

Mobile real-time EEG imaging Bayesian inference with sparse, temporally smooth source priors

EEG based real-time imaging of human brain function has many potential applications including quality control, in-line experimental design, brain state decoding, and neuro-feedback. In mobile applications these possibilities are attractive as elements in systems for personal state monitoring and well-being, and in clinical settings were patients may need imaging under quasi-natural conditions. Challenges related to the ill-posed nature of the EEG imaging problem escalate in mobile real-time systems and new algorithms and the use of meta-data may be necessary to succeed. Based on recent work (Delorme et al., 2011) we hypothesize that solutions of interest are sparse. We propose a new Markovian prior for temporally sparse solutions and a direct search for sparse solutions as implemented by the so-called “variational garrote” (Kappen, 2011). We show that the new prior and inference scheme leads to improved solutions over competing sparse Bayesian schemes based on the “multiple measurement vectors” approach.

Fusing Simultaneous EEG and fMRI Using Functional and Anatomical Information

Simultaneously measuring electro physical and hemodynamic signals has become more accessible in the last years and the need for modeling techniques that can fuse the modalities is growing. In this work we augment a specific fusion method, the multimodal Source Power Co-modulation (mSPoC), to not only use functional but also anatomical information. The goal is to extract correlated source components from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). Anatomical information enters our proposed extension to mSPoC via the forward model, which relates the activity on cortex level to the EEG sensors. The augmented mSPoC is shown to outperform the original version in realistic simulations where the signal to noise ratio is low or where training epochs are scarce.

EEG Source Reconstruction using Sparse Basis Function Representations

State of the art performance of 3D EEG imaging is based on reconstruction using spatial basis function repre-sentations. In this work we augment the Variational Garrote (VG) approach for sparse approximation to incorporate spatial basis functions. As VG handles the bias variance trade-off with cross-validation this approach is more automated than competing approaches such as Multiple Sparse Priors (Friston et al., 2008) or Champagne (Wipf et al., 2010) that require manual selection of noise level and auxiliary signal free data, respectively. Finally, we propose an unbiased estimator of the reproducibility of the reconstructed activation time course based on a split-half resampling protocol.

EEG source imaging assists decoding in a face recognition task

EEG based brain state decoding has numerous applications. State of the art decoding is based on processing of the multivariate sensor space signal, however evidence is mounting that EEG source reconstruction can assist decoding. EEG source imaging leads to high-dimensional representations and rather strong a priori information must be invoked. Recent work by Edelman et al. (2016) has demonstrated that introduction of a spatially focal source space representation can improve decoding of motor imagery. In this work we explore the generality of Edelman et al. hypothesis by considering decoding of face recognition. This task concerns the differentiation of brain responses to images of faces and scrambled faces and poses a rather difficult decoding problem at the single trial level. We implement the pipeline using spatially focused features and show that this approach is challenged and source imaging does not lead to an improved decoding. We design a distributed pipeline in which the classifier has access to brain wide features which in turn does lead to a 15% reduction in the error rate using source space features. Hence, our work presents supporting evidence for the hypothesis that source imaging improves decoding.

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

Abstract Electroencephalography (EEG) can capture brain dynamics in high temporal resolution. By projecting the scalp EEG signal back to its origin in the brain also high spatial resolution can be achieved. Source localized EEG therefore has potential to be a very powerful tool for understanding the functional dynamics of the brain. Solving the inverse problem of EEG is however highly ill‐posed as there are many more potential locations of the EEG generators than EEG measurement points. Several well‐known properties of brain dynamics can be exploited to alleviate this problem. More short ranging connections exist in the brain than long ranging, arguing for spatially focal sources. Additionally, recent work (Delorme et al., 2012) argues that EEG can be decomposed into components having sparse source distributions. On the temporal side both short and long term stationarity of brain activation are seen. We summarize these insights in an inverse solver, the so‐called “Variational Garrote” (Kappen and Gómez, 2013). Using a Markov prior we can incorporate flexible degrees of temporal stationarity. Through spatial basis functions spatially smooth distributions are obtained. Sparsity of these are inherent to the Variational Garrote solver. We name our method the MarkoVG and demonstrate its ability to adapt to the temporal smoothness and spatial sparsity in simulated EEG data. Finally a benchmark EEG dataset is used to demonstrate MarkoVGs ability to recover non‐stationary brain dynamics. Graphical abstract Figure. No caption available. HighlightsMarkoVG solves the EEG inverse problem using relevant physiological priors.Variational Bayes inference allows identification of sparse source distributions.Spatial basis functions are used to produce locally smooth activation.A Markov prior enables inference of the temporal smoothness of the activation states (active vs. inactive dipoles).By imposing smoothness in the activation state rather than in the dipole strength, high frequency temporal dynamics is preserved.