Sequential Monte Carlo samplers for semilinear inverse problems and application to magnetoencephalography

We discuss the use of a recent class of sequential Monte Carlo methods for solving inverse problems characterized by a semi-linear structure, i.e. where the data depend linearly on a subset of variables and nonlinearly on the remaining ones. In this type of problems, under proper Gaussian assumptions one can marginalize the linear variables. This means that the Monte Carlo procedure needs only to be applied to the nonlinear variables, while the linear ones can be treated analytically; as a result, the Monte Carlo variance and/or the computational cost decrease. We use this approach to solve the inverse problem of magnetoencephalography, with a multi-dipole model for the sources. Here, data depend nonlinearly on the number of sources and their locations, and depend linearly on their current vectors. The semi-analytic approach enables us to estimate the number of dipoles and their location from a whole time-series, rather than a single time point, while keeping a low computational cost.Comment: 26 pages, 6 figure

Iterative algorithms for a non-linear inverse problem in atmospheric lidar

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms outperform standard methods in terms of sensitivity to noise and reliability of the estimated profile.Comment: 19 pages, 6 figure

Bayesian multi--dipole localization and uncertainty quantification from simultaneous EEG and MEG recordings

We deal with estimation of multiple dipoles from combined MEG and EEG time--series. We use a sequential Monte Carlo algorithm to characterize the posterior distribution of the number of dipoles and their locations. By considering three test cases, we show that using the combined data the method can localize sources that are not easily (or not at all) visible with either of the two individual data alone. In addition, the posterior distribution from combined data exhibits a lower variance, i.e. lower uncertainty, than the posterior from single device.Comment: 4 pages, 3 figures -- conference paper from EMBEC 2017, Tampere, Finlan

Chapter Statistical Approaches to the Inverse Problem

Communications engineering / telecommunication

Efficient abstraction of clock synchronization at the operating system level

Distributed embedded systems are emerging and gaining importance in various domains, including industrial control applications where time determinism – hence network clock synchronization – is fundamental. In modern applications, moreover, this core functionality is required by many different software components, from OS kernel and radio stack up to applications. An abstraction layer devoted to handling time needs therefore introducing, and to encapsulate time corrections at the lowest possible level, the said layer should take the form of a timer device driver offering a Virtual Clock to the entire system. In this paper we show that doing so introduces a nonlinearity in the dynamics of the clock, and we design a controller based on feedback linearization to handle the issue. To put the idea to work, we extend the Miosix RTOS with a generic interface allowing to implement virtual clocks, including the newly designed controller that we call FLOPSYNC-3 after its ancestor. Also, we introduce the resulting virtual clock in the TDMH [20] real-time wireless mesh protocol

Bayesian Multi--Dipole Modeling of a Single Topography in MEG by Adaptive Sequential Monte Carlo Samplers

In the present paper, we develop a novel Bayesian approach to the problem of estimating neural currents in the brain from a fixed distribution of magnetic field (called \emph{topography}), measured by magnetoencephalography. Differently from recent studies that describe inversion techniques, such as spatio-temporal regularization/filtering, in which neural dynamics always plays a role, we face here a purely static inverse problem. Neural currents are modelled as an unknown number of current dipoles, whose state space is described in terms of a variable--dimension model. Within the resulting Bayesian framework, we set up a sequential Monte Carlo sampler to explore the posterior distribution. An adaptation technique is employed in order to effectively balance the computational cost and the quality of the sample approximation. Then, both the number and the parameters of the unknown current dipoles are simultaneously estimated. The performance of the method is assessed by means of synthetic data, generated by source configurations containing up to four dipoles. Eventually, we describe the results obtained by analyzing data from a real experiment, involving somatosensory evoked fields, and compare them to those provided by three other methods.Comment: 20 pages, 4 figure

Dynamic filtering of static dipoles in magnetoencephalography

We consider the problem of estimating neural activity from measurements of the magnetic fields recorded by magnetoencephalography. We exploit the temporal structure of the problem and model the neural current as a collection of evolving current dipoles, which appear and disappear, but whose locations are constant throughout their lifetime. This fully reflects the physiological interpretation of the model. In order to conduct inference under this proposed model, it was necessary to develop an algorithm based around state-of-the-art sequential Monte Carlo methods employing carefully designed importance distributions. Previous work employed a bootstrap filter and an artificial dynamic structure where dipoles performed a random walk in space, yielding nonphysical artefacts in the reconstructions; such artefacts are not observed when using the proposed model. The algorithm is validated with simulated data, in which it provided an average localisation error which is approximately half that of the bootstrap filter. An application to complex real data derived from a somatosensory experiment is presented. Assessment of model fit via marginal likelihood showed a clear preference for the proposed model and the associated reconstructions show better localisation

Dealing with Uncertainty in Lexical Annotation

We present ALA, a tool for the automatic lexical annotation (i.e.annotation w.r.t. a thesaurus/lexical resource) of structured and semi-structured data sources and the discovery of probabilistic lexical relationships in a data integration environment. ALA performs automatic lexical annotation through the use of probabilistic annotations, i.e. an annotation is associated to a probability value. By performing probabilistic lexical annotation, we discover probabilistic inter-sources lexical relationships among schema elements. ALA extends the lexical annotation module of the MOMIS data integration system. However, it may be applied in general in the context of schema mapping discovery, ontology merging and data integration system and it is particularly suitable for performing “on-the-fly” data integration or probabilistic ontology matching

A Novel Quick and Easy Test for Radial Artery Occlusion With the Laser Doppler Scan

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