Alexandra Koulouri

Joonas Lahtinen, Alexandra Koulouri

Electroencephalography (EEG) source imaging aims to reconstruct the spatial distribution of neural activity within the brain from non-invasive scalp measurements. This inverse problem is severely ill-posed due to the low spatial resolution of EEG and the presence of measurement noise, necessitating robust regularization techniques. Bayesian approaches provide a principled framework for incorporating prior knowledge into the solution, where regularization naturally arises through prior distributions and their associated hyperparameters. In this work, we provide an overview of key Bayesian methods for EEG source imaging based on Gaussian, Laplace, and group Laplace priors, with particular emphasis on hierarchical models that promote sparsity. We analyze the connections between these hierarchical formulations and classical optimization techniques, and provide an analytical description of their implementation using expectation -maximization and alternating optimization algorithms. To address the issue of depth bias where deeper sources are systematically underestimated or mislocalized - we extend a statistical signal-to-noise ratio (SNR) framework to derive depth-weighted priors that account for differences in how strongly sources at different depths are reflected in the measurements. Finally, we illustrate the behaviour of the considered models through simulation studies involving sources at varying depths. The results highlight the impact of prior selection and depth weighting on reconstruction accuracy and demonstrate the importance of informed model design for depth-sensitive EEG source localization.

Alexandra Koulouri

In this paper, we propose a Bayesian framework to create two dimensional ionospheric images of high spatio-temporal resolution to monitor ionospheric irregularities as measured by the S4 index. Here, we recast the standard Bayesian recursive filtering for a linear Gaussian state-space model, also referred to as the Kalman filter, first by augmenting the (pierce point) observation model with connectivity information stemming from the insight and assumptions/standard modeling about the spatial distribution of the scintillation activity on the ionospheric shell at 350 km altitude. Thus, we achieve to handle the limited spatio-temporal observations. Then, by introducing a set of Kalman filters running in parallel, we mitigate the uncertainty related to a tuning parameter of the proposed augmented model. The output images are a weighted average of the state estimates of the individual filters. We demonstrate our approach by rendering two dimensional real-time ionospheric images of S4 amplitude scintillation at 350 km over South America with temporal resolution of one minute. Furthermore, we employ extra S4 data that was not used in producing these ionospheric images, to check and verify the ability of our images to predict this extra data in particular ionospheric pierce points. Our results show that in areas with a network of ground receivers with a relatively good coverage (e.g. within a couple of kilometers distance) the produced images can provide reliable real-time results. Our proposed algorithmic framework can be readily used to visualize real-time ionospheric images taking as inputs the available scintillation data provided from freely available web-servers.

Alexandra Koulouri, Ville Rimpilainen

The electroencephalography (EEG) source imaging problem is very sensitive to the electrical modelling of the skull of the patient under examination. Unfortunately, the currently available EEG devices and their embedded software do not take this into account; instead, it is common to use a literature-based skull conductivity parameter. In this paper, we propose a statistical method based on the Bayesian approximation error approach to compensate for source imaging errors due to the unknown skull conductivity and, simultaneously, to compute a low-order estimate for the actual skull conductivity value. By using simulated EEG data that corresponds to focal source activity, we demonstrate the potential of the method to reconstruct the underlying focal sources and low-order errors induced by the unknown skull conductivity. Subsequently, the estimated errors are used to approximate the skull conductivity. The results indicate clear improvements in the source localization accuracy and feasible skull conductivity estimates.