A unified weighted minimum norm solution for the reference inverse problem in EEG.

A well known problem in EEG recordings deals with the unknown potential of the reference electrode. In the last years several authors presented comparisons among the most popular solutions, the global conclusion being that the traditional Average Reference (AR) and the Reference Standardization Technique (REST) are the best approximations (Nunez, 2010; Kayser and Tenke, 2010; Liu et al., 2015; Chella et al., 2016). In this work we do not aim to further compare these techniques but to support the fact that both solutions can be derived from a general inverse problem formalism for reference estimation (Hu et al., 2019; Hu et al., 2018; Salido-Ruiz et al., 2011). Using the alternative approach of least squares, our findings are consistent with the theoretical findings in Hu et al. (2019) and Hu et al. (2018) showing that the AR is the minimum norm solution, while REST is a weighted minimum norm including some approximate propagation model. AR is thus a particular case of REST, which itself uses a particular formulation of the source estimation inverse problem. With a different derivation, we provide the additional powerful evidences to reinforce the cited findings.

A Space-Time-Frequency Dictionary for Sparse Cortical Source Localization.

OBJECTIVE: Cortical source imaging aims at identifying activated cortical areas on the surface of the cortex from the raw electroencephalogram (EEG) data. This problem is ill posed, the number of channels being very low compared to the number of possible source positions. METHODS: In some realistic physiological situations, the active areas are sparse in space and of short time durations, and the amount of spatio-temporal data to carry the inversion is then limited. In this study, we propose an original data driven space-time-frequency (STF) dictionary which takes into account simultaneously both spatial and time-frequency sparseness while preserving smoothness in the time frequency (i.e., nonstationary smooth time courses in sparse locations). Based on these assumptions, we take benefit of the matching pursuit (MP) framework for selecting the most relevant atoms in this highly redundant dictionary. RESULTS: We apply two recent MP algorithms, single best replacement (SBR) and source deflated matching pursuit, and we compare the results using a spatial dictionary and the proposed STF dictionary to demonstrate the improvements of our multidimensional approach. We also provide comparison using well-established inversion methods, FOCUSS and RAP-MUSIC, analyzing performances under different degrees of nonstationarity and signal to noise ratio. CONCLUSION: Our STF dictionary combined with the SBR approach provides robust performances on realistic simulations. From a computational point of view, the algorithm is embedded in the wavelet domain, ensuring high efficiency in term of computation time. SIGNIFICANCE: The proposed approach ensures fast and accurate sparse cortical localizations on highly nonstationary and noisy data.

Sparse cortical source localization using spatio-temporal atoms.

This paper addresses the problem of sparse localization of cortical sources from scalp EEG recordings. Localization algorithms use propagation model under spatial and/or temporal constraints, but their performance highly depends on the data signal-to-noise ratio (SNR). In this work we propose a dictionary based sparse localization method which uses a data driven spatio-temporal dictionary to reconstruct the measurements using Single Best Replacement (SBR) and Continuation Single Best Replacement (CSBR) algorithms. We tested and compared our methods with the well-known MUSIC and RAP-MUSIC algorithms on simulated realistic data. Tests were carried out for different noise levels. The results show that our method has a strong advantage over MUSIC-type methods in case of synchronized sources.

Fall detection algorithm in energy efficient multistate sensor system.

Health issues for elderly people may lead to different injuries obtained during simple activities of daily living (ADL). Potentially the most dangerous are unintentional falls that may be critical or even lethal to some patients due to the heavy injury risk. Many fall detection systems are proposed but only recently such health care systems became available. Nevertheless sensor design, accuracy as well as energy consumption efficiency can be improved. In this paper we present a single 3-axial accelerometer energy-efficient sensor system. Power saving is achieved by selective event processing triggered by fall detection procedure. The results in our simulations show 100% accuracy when the threshold parameters are chosen correctly. Estimated energy consumption seems to extend battery life significantly.

Combining bayesian source imaging with equivalent dipole approach to solve the intracranial EEG source localization problem.

The brain source localization problem has been extensively studied in the past years, yielding a large panel of methodologies, each bringing their own strengths and weaknesses. Combining several of these approaches might help in enhancing their respective performance. Our study is carried out in the particular context of intracranial recordings, with the objective to explain the measurements based on a reduced number of dipolar activities. We take benefit of the sparse nature of the Bayesian approaches to separate the noise from the source space, and to distinguish between several source contributions on the electrodes. This first step provides accurate estimates of the dipole projections, which can be used as an entry to an equivalent current dipole fitting procedure. We demonstrate on simulations that the localization results are significantly enhanced by this post-processing step when up to five dipoles are activated simultaneously.

Dipolar estimates of the cortical map.

Various methods based on anatomical or mathematical models have been developed to estimate cortical potentials. Among them, the most popular are the surface Laplacians (SL) and the Electrical Source Imaging (ESI) approaches. In this paper, we develop an informed method named dipolar cortical mapping (DCM), aiming to find a balance between ESI methods based on anatomical models and methods without strong anatomical priors, such as surface Laplacians. Our method only uses easily available information on the electrode position and is based on a physiologically parametrized family of interpolating functions. Simulation results show that DCM competes with previously proposed surface Laplacians and with the model based Minimum Norm Estimates (MNE) computed with a Boundary Element Model (BEM).

Smoothness constraint for cortical dipolar sources estimation.

In the last decade, a wide range of approaches have been proposed to estimate the activity of physiological sources from multi-channel electroencephalographic (EEG) data. Two utterly different directions can be distinguished: brain source imaging (BSI) and blind source separation (BSS). While the first approach is based on the inversion of a given forward model, the latter blindly decomposes the EEG mixing by optimization of a contrast function excluding any physiological priors on the problem. All these methods have proven their ability in reconstructing efficiently the source activities in some well adapted situations. Nevertheless, the synthesis of a reliable lead field model for BSI is computationally demanding, and the criterion to be optimized in BSS are often inadequate with regards to the physiology of the problem. In this paper, a compromise between these two methodological trends is introduced. A BSS method is described taking account of physiological knowledge on the projection of the sources on the scalp map in conjunction with strong priors on the localization of the recorded sources. This estimation method is demonstrated to lead to a generalization of the classical Hjorth's laplacian montage, and provides satisfactory simulation results when the appropriate configurations on the sources are met.