Bayesian M/EEG source localization with possible joint skull conductivity estimation

M/EEG mechanisms allow determining changes in the brain activity, which is useful in diagnosing brain disorders such as epilepsy. They consist of measuring the electric potential at the scalp and the magnetic field around the head. The measurements are related to the underlying brain activity by a linear model that depends on the lead-field matrix. Localizing the sources, or dipoles, of M/EEG measurements consists of inverting this linear model. However, the non-uniqueness of the solution (due to the fundamental law of physics) and the low number of dipoles make the inverse problem ill-posed. Solving such problem requires some sort of regularization to reduce the search space. The literature abounds of methods and techniques to solve this problem, especially with variational approaches. This thesis develops Bayesian methods to solve ill-posed inverse problems, with application to M/EEG. The main idea underlying this work is to constrain sources to be sparse. This hypothesis is valid in many applications such as certain types of epilepsy. We develop different hierarchical models to account for the sparsity of the sources. Theoretically, enforcing sparsity is equivalent to minimizing a cost function penalized by an l0 pseudo norm of the solution. However, since the l0 regularization leads to NP-hard problems, the l1 approximation is usually preferred. Our first contribution consists of combining the two norms in a Bayesian framework, using a Bernoulli-Laplace prior. A Markov chain Monte Carlo (MCMC) algorithm is used to estimate the parameters of the model jointly with the source location and intensity. Comparing the results, in several scenarios, with those obtained with sLoreta and the weighted l1 norm regularization shows interesting performance, at the price of a higher computational complexity. Our Bernoulli-Laplace model solves the source localization problem at one instant of time. However, it is biophysically well-known that the brain activity follows spatiotemporal patterns. Exploiting the temporal dimension is therefore interesting to further constrain the problem. Our second contribution consists of formulating a structured sparsity model to exploit this biophysical phenomenon. Precisely, a multivariate Bernoulli-Laplacian distribution is proposed as an a priori distribution for the dipole locations. A latent variable is introduced to handle the resulting complex posterior and an original Metropolis-Hastings sampling algorithm is developed. The results show that the proposed sampling technique improves significantly the convergence. A comparative analysis of the results is performed between the proposed model, an l21 mixed norm regularization and the Multiple Sparse Priors (MSP) algorithm. Various experiments are conducted with synthetic and real data. Results show that our model has several advantages including a better recovery of the dipole locations. The previous two algorithms consider a fully known leadfield matrix. However, this is seldom the case in practical applications. Instead, this matrix is the result of approximation methods that lead to significant uncertainties. Our third contribution consists of handling the uncertainty of the lead-field matrix. The proposed method consists in expressing this matrix as a function of the skull conductivity using a polynomial matrix interpolation technique. The conductivity is considered as the main source of uncertainty of the lead-field matrix. Our multivariate Bernoulli-Laplacian model is then extended to estimate the skull conductivity jointly with the brain activity. The resulting model is compared to other methods including the techniques of Vallaghé et al and Guttierez et al. Our method provides results of better quality without requiring knowledge of the active dipole positions and is not limited to a single dipole activation

Bayesian inference for structured additive regression models for large-scale problems with applications to medical imaging

In der angewandten Statistik können Regressionsmodelle mit hochdimensionalen Koeffizienten auftreten, die sich nicht mit gewöhnlichen Computersystemen schätzen lassen. Dies betrifft unter anderem die Analyse digitaler Bilder unter Berücksichtigung räumlich-zeitlicher Abhängigkeiten, wie sie innerhalb der medizinisch-biologischen Forschung häufig vorkommen. In der vorliegenden Arbeit wird ein Verfahren formuliert, das in der Lage ist, Regressionsmodelle mit hochdimensionalen Koeffizienten und nicht-normalverteilten Zielgrößen unter moderaten Anforderungen an die benötigte Hardware zu schätzen. Hierzu wird zunächst im Rahmen strukturiert additiver Regressionsmodelle aufgezeigt, worin die Limitationen aktueller Inferenzansätze bei der Anwendung auf hochdimensionale Problemstellungen liegen, sowie Möglichkeiten diskutiert, diese zu umgehen. Darauf basierend wird ein Algorithmus formuliert, dessen Stärken und Schwächen anhand von Simulationsstudien analysiert werden. Darüber hinaus findet das Verfahren Anwendung in drei verschiedenen Bereichen der medizinisch-biologischen Bildgebung und zeigt dadurch, dass es ein vielversprechender Kandidat für die Beantwortung hochdimensionaler Fragestellungen ist.In applied statistics regression models with high-dimensional coefficients can occur which cannot be estimated using ordinary computers. Amongst others, this applies to the analysis of digital images taking spatio-temporal dependencies into account as they commonly occur within bio-medical research. In this thesis a procedure is formulated which allows to fit regression models with high-dimensional coefficients and non-normal response values requiring only moderate computational equipment. To this end, limitations of different inference strategies for structured additive regression models are demonstrated when applied to high-dimensional problems and possible solutions are discussed. Based thereon an algorithm is formulated whose strengths and weaknesses are subsequently analyzed using simulation studies. Furthermore, the procedure is applied to three different fields of bio-medical imaging from which can be concluded that the algorithm is a promising candidate for answering high-dimensional problems

Bayesian inversion in biomedical imaging

Biomedizinische Bildgebung ist zu einer Schlüsseltechnik geworden, Struktur oder Funktion lebender Organismen nicht-invasiv zu untersuchen. Relevante Informationen aus den gemessenen Daten zu rekonstruieren erfordert neben mathematischer Modellierung und numerischer Simulation das verlässliche Lösen schlecht gestellter inverser Probleme. Um dies zu erreichen müssen zusätzliche a-priori Informationen über die zu rekonstruierende Größe formuliert und in die algorithmischen Lösungsverfahren einbezogen werden. Bayesianische Invertierung ist eine spezielle mathematische Methodik dies zu tun. Die vorliegende Arbeit entwickelt eine aktuelle Übersicht Bayesianischer Invertierung und demonstriert die vorgestellten Konzepte und Algorithmen in verschiedenen numerischen Studien, darunter anspruchsvolle Anwendungen aus der biomedizinischen Bildgebung mit experimentellen Daten. Ein Schwerpunkt liegt dabei auf der Verwendung von Dünnbesetztheit/Sparsity als a-priori Information.Biomedical imaging techniques became a key technology to assess the structure or function of living organisms in a non-invasive way. Besides innovations in the instrumentation, the development of new and improved methods for processing and analysis of the measured data has become a vital field of research. Building on traditional signal processing, this area nowadays also comprises mathematical modeling, numerical simulation and inverse problems. The latter describes the reconstruction of quantities of interest from measured data and a given generative model. Unfortunately, most inverse problems are ill-posed, which means that a robust and reliable reconstruction is not possible unless additional a-priori information on the quantity of interest is incorporated into the solution method. Bayesian inversion is a mathematical methodology to formulate and employ a-priori information in computational schemes to solve the inverse problem. This thesis develops a recent overview on Bayesian inversion and exemplifies the presented concepts and algorithms in various numerical studies including challenging biomedical imaging applications with experimental data. A particular focus is on using sparsity as a-priori information within the Bayesian framework. <br

Bayesian inference for structured additive regression models for large-scale problems with applications to medical imaging

In der angewandten Statistik können Regressionsmodelle mit hochdimensionalen Koeffizienten auftreten, die sich nicht mit gewöhnlichen Computersystemen schätzen lassen. Dies betrifft unter anderem die Analyse digitaler Bilder unter Berücksichtigung räumlich-zeitlicher Abhängigkeiten, wie sie innerhalb der medizinisch-biologischen Forschung häufig vorkommen. In der vorliegenden Arbeit wird ein Verfahren formuliert, das in der Lage ist, Regressionsmodelle mit hochdimensionalen Koeffizienten und nicht-normalverteilten Zielgrößen unter moderaten Anforderungen an die benötigte Hardware zu schätzen. Hierzu wird zunächst im Rahmen strukturiert additiver Regressionsmodelle aufgezeigt, worin die Limitationen aktueller Inferenzansätze bei der Anwendung auf hochdimensionale Problemstellungen liegen, sowie Möglichkeiten diskutiert, diese zu umgehen. Darauf basierend wird ein Algorithmus formuliert, dessen Stärken und Schwächen anhand von Simulationsstudien analysiert werden. Darüber hinaus findet das Verfahren Anwendung in drei verschiedenen Bereichen der medizinisch-biologischen Bildgebung und zeigt dadurch, dass es ein vielversprechender Kandidat für die Beantwortung hochdimensionaler Fragestellungen ist.In applied statistics regression models with high-dimensional coefficients can occur which cannot be estimated using ordinary computers. Amongst others, this applies to the analysis of digital images taking spatio-temporal dependencies into account as they commonly occur within bio-medical research. In this thesis a procedure is formulated which allows to fit regression models with high-dimensional coefficients and non-normal response values requiring only moderate computational equipment. To this end, limitations of different inference strategies for structured additive regression models are demonstrated when applied to high-dimensional problems and possible solutions are discussed. Based thereon an algorithm is formulated whose strengths and weaknesses are subsequently analyzed using simulation studies. Furthermore, the procedure is applied to three different fields of bio-medical imaging from which can be concluded that the algorithm is a promising candidate for answering high-dimensional problems

Dynamic Thermal Imaging for Intraoperative Monitoring of Neuronal Activity and Cortical Perfusion

Neurosurgery is a demanding medical discipline that requires a complex interplay of several neuroimaging techniques. This allows structural as well as functional information to be recovered and then visualized to the surgeon. In the case of tumor resections this approach allows more fine-grained differentiation of healthy and pathological tissue which positively influences the postoperative outcome as well as the patient's quality of life. In this work, we will discuss several approaches to establish thermal imaging as a novel neuroimaging technique to primarily visualize neural activity and perfusion state in case of ischaemic stroke. Both applications require novel methods for data-preprocessing, visualization, pattern recognition as well as regression analysis of intraoperative thermal imaging. Online multimodal integration of preoperative and intraoperative data is accomplished by a 2D-3D image registration and image fusion framework with an average accuracy of 2.46 mm. In navigated surgeries, the proposed framework generally provides all necessary tools to project intraoperative 2D imaging data onto preoperative 3D volumetric datasets like 3D MR or CT imaging. Additionally, a fast machine learning framework for the recognition of cortical NaCl rinsings will be discussed throughout this thesis. Hereby, the standardized quantification of tissue perfusion by means of an approximated heating model can be achieved. Classifying the parameters of these models yields a map of connected areas, for which we have shown that these areas correlate with the demarcation caused by an ischaemic stroke segmented in postoperative CT datasets. Finally, a semiparametric regression model has been developed for intraoperative neural activity monitoring of the somatosensory cortex by somatosensory evoked potentials. These results were correlated with neural activity of optical imaging. We found that thermal imaging yields comparable results, yet doesn't share the limitations of optical imaging. In this thesis we would like to emphasize that thermal imaging depicts a novel and valid tool for both intraoperative functional and structural neuroimaging

EEG source localization based on a structured sparsity prior and a partially collapsed Gibbs sampler

International audienceIn this paper, we propose a hierarchical Bayesian model approximating the ℓ20 mixed-norm regularization by a multivariate Bernoulli Laplace prior to solve the EEG inverse problem by promoting spatial structured sparsity. The posterior distribution of this model is too complex to derive closed-form expressions of the standard Bayesian estimators. An MCMC method is proposed to sample this posterior and estimate the model parameters from the generated samples. The algorithm is based on a partially collapsed Gibbs sampler and a dual dipole random shift proposal for the non-zero positions. The brain activity and all other model parameters are jointly estimated in a completely unsupervised framework. The results obtained on synthetic data with controlled ground truth show the good performance of the proposed method when compared to the ℓ21 approach in different scenarios, and its capacity to estimate point-like source activity

Nonparametric Bayesian methods in robotic vision

In this dissertation non-parametric Bayesian methods are used in the application of robotic vision. Robots make use of depth sensors that represent their environment using point clouds. Non-parametric Bayesian methods can (1) determine how good an object is recognized, and (2) determine how many objects a particular scene contains. When there is a model available for the object to be recognized and the nature of perceptual error is known, a Bayesian method will act optimally.In this dissertation Bayesian models are developed to represent geometric objects such as lines and line segments (consisting out of points). The infinite line model and the infinite line segment model use a non-parametric Bayesian model, to be precise, a Dirichlet process, to represent the number of objects. The line or the line segment is represented by a probability distribution. The lines can be represented by conjugate distributions and then Gibbs sampling can be used. The line segments are not represented by conjugate distributions and therefore a split-merge sampler is used.A split-merge sampler fits line segments by assigning points to a hypothetical line segment. Then it proposes splits of a single line segment or merges of two line segments. A new sampler, the triadic split-merge sampler, introduces steps that involve three line segments. In this dissertation, the new sampler is compared to a conventional split-merge sampler. The triadic sampler can be applied to other problems as well, i.e., not only problems in robotic perception.The models for objects can also be learned. In the dissertation this is done for more complex objects, such as cubes, built up out of hundreds of points. An auto-encoder then learns to generate a representative object given the data. The auto-encoder uses a newly defined reconstruction distance, called the partitioning earth mover’s distance. The object that is learned by the auto-encoder is used in a triadic sampler to (1) identify the point cloud objects and to (2) establish multiple occurrences of those objects in the point cloud.Algorithms and the Foundations of Software technolog

Contributions au traitement des images multivariées

Ce mémoire résume mon activité pédagogique et scientifique en vue de l’obtention de l’habilitation à diriger des recherches

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio