Compensation of domain modelling errors in the inverse source problem of the Poisson equation: Application in electroencephalographic imaging

Koulouri, Alexandra; Rimpiläinen, Ville; Brookes, Mike; Kaipio, Jari P.

doi:10.1016/j.apnum.2016.01.005

Cited by 12 publications

(9 citation statements)

References 51 publications

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“…In our analysis the head geometry was considered fully known; however, it can also be taken into account as an uncertainty [14]. We also note that in this work we estimated a single conductivity value for the whole skull.…”

Section: Results Discussion and Future Workmentioning

confidence: 99%

Simultaneous Skull Conductivity and Focal Source Imaging from EEG Recordings with the help of Bayesian Uncertainty Modelling

Koulouri¹,

Rimpiläinen²

2020

Preprint

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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 loworder 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.

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Section: Results Discussion and Future Workmentioning

confidence: 99%

Simultaneous Skull Conductivity and Focal Source Imaging from EEG Recordings with the help of Bayesian Uncertainty Modelling

Koulouri¹,

Rimpiläinen²

2020

Preprint

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“…Different ways to tackle the problem of working with an incorrect model in Bayesian framework have been suggested in the literature. The Bayesian approach allows us also to treat problems that depend on unknown or poorly known model parameters, including uncertainties in the modeling geometry (Koulouri, Rimpiläinen, Brookes, & Kaipio, 2016) or incompletely modeled physics (Gulley, Kaipio, Eccles, & Malin, 2017).…”

Section: Model Uncertaintiesmentioning

confidence: 99%

Inverse problems: From regularization to Bayesian inference

Calvetti

Somersalo

2018

WIREs Computational Stats

110

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Inverse problems deal with the quest for unknown causes of observed consequences, based on predictive models, known as the forward models, that associate the former quantities to the latter in the causal order. Forward models are usually well‐posed, as causes determine consequences in a unique and stable way. Inverse problems, on the other hand, are usually ill‐posed: the data may be insufficient to identify the cause unambiguously, an exact solution may not exist, and, like in a mystery story, discovering the cause without extra information tends to be highly sensitive to measurement noise and modeling errors. The Bayesian methodology provides a versatile and natural way of incorporating extra information to supplement the noisy data by modeling the unknown as a random variable to highlight the uncertainty about its value. Presenting the solution in the form of a posterior distribution provides a wide range of possibilities to compute useful estimates. Inverse problems are traditionally approached from the point of view of regularization, a process whereby the ill‐posed problem is replaced by a nearby well‐posed one. While many of the regularization techniques can be reinterpreted in the Bayesian framework through prior design, the Bayesian formalism provides new techniques to enrich the paradigm of traditional inverse problems. In particular, inaccuracies and inadequacies of the forward model are naturally handled in the statistical framework. Similarly, qualitative information about the solution may be reformulated in the form of priors with unknown parameters that can be successfully handled in the hierarchical Bayesian context. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Algorithms and Computational Methods > Numerical Methods Applications of Computational Statistics > Computational Mathematics

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“…Previously, the BAE approach has been successfully used, for example, in EIT [30,31,32] and optical tomography [33,34,35]. In EEG source imaging, the BAE approach has been shown to alleviate localization errors arising from the unknown head geometry by using simulated 2-dimensional finite element (FE) models [36].…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…In this paper, we chose to address the well-known problem of unknown skull conductivity. In addition to this, BAE can be used to treat other unknown (or uncertain) forward model parameters, such as the geometry of the head [36]. Moreover, the properties of the EEG electrodes are typically not modelled accurately and for instance their contact impedances are only poorly known [53,54].…”

Section: Transferability Of Bayesian Uncertainty Modellingmentioning

confidence: 99%

Improved EEG source localization with Bayesian uncertainty modelling of unknown skull conductivity

et al. 2019

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Electroencephalography (EEG) source imaging is an ill-posed inverse problem that requires accurate conductivity modelling of the head tissues, especially the skull. Unfortunately, the conductivity values are difficult to determine in vivo. In this paper, we show that the exact knowledge of the skull conductivity is not always necessary when the Bayesian approximation error (BAE) approach 5 is exploited. In BAE, we first postulate a probability distribution for the skull conductivity that describes our (lack of) knowledge on its value, and model the effects of this uncertainty on EEG recordings with the help of an additive error term in the observation model. Before the Bayesian inference, the likelihood is marginalized over this error term. Thus, in the inversion we estimate only our 10 primary unknown, the source distribution. We quantified the improvements in the source localization when the proposed Bayesian modelling was used in the presence of different skull conductivity errors and levels of measurement noise. Based on the results, BAE was able to improve the source localization accuracy, particularly when the unknown (true) skull conductivity was much lower than

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Compensation of domain modelling errors in the inverse source problem of the Poisson equation: Application in electroencephalographic imaging

Cited by 12 publications

References 51 publications

Simultaneous Skull Conductivity and Focal Source Imaging from EEG Recordings with the help of Bayesian Uncertainty Modelling

Simultaneous Skull Conductivity and Focal Source Imaging from EEG Recordings with the help of Bayesian Uncertainty Modelling

Inverse problems: From regularization to Bayesian inference

Improved EEG source localization with Bayesian uncertainty modelling of unknown skull conductivity

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