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A solution to the dynamical inverse problem of EEG generation using spatiotemporal Kalman filtering

Andreas Galka, Okito Yamashita, Tohru Ozaki, Rolando Biscay, Pedro Valdés-Sosa
2004 NeuroImage  
We present a new approach for estimating solutions of the dynamical inverse problem of EEG generation.  ...  In contrast to previous approaches, we reinterpret this problem as a filtering problem in a state space framework; for the purpose of its solution, we propose a new extension of Kalman filtering to the  ...  Clinical EEG data was kindly provided by U. Stephani and H. Muhle from the Neuropediatric Hospital of the University of Kiel, Germany.  ... 
doi:10.1016/j.neuroimage.2004.02.022 pmid:15488394 fatcat:vecvm5mzwzhzhd2nyhij7h2ha4

GARCH modelling of covariance in dynamical estimation of inverse solutions

Andreas Galka, Okito Yamashita, Tohru Ozaki
2004 Physics Letters A  
The problem of estimating unobserved states of spatially extended dynamical systems poses an inverse problem, which can be solved approximately by a recently developed variant of Kalman filtering; in order  ...  to provide the model of the dynamics with more flexibility with respect to space and time, we suggest to combine the concept of GARCH modelling of covariance, well known in econometrics, with Kalman filtering  ...  The Kalman filter is the natural tool for estimating unobserved states in dynamical systems [17] ; nevertheless, only a small number of applications of Kalman filtering to inverse problems have been reported  ... 
doi:10.1016/j.physleta.2004.10.045 fatcat:cpmw6lt4jnbh3jovd5ejl2lsje

Recursive penalized least squares solution for dynamical inverse problems of EEG generation

Okito Yamashita, Andreas Galka, Tohru Ozaki, Rolando Biscay, Pedro Valdes-Sosa
2004 Human Brain Mapping  
In the dynamical inverse problem of electroencephalogram (EEG) generation where a specific dynamics for the electrical current distribution is assumed, we can impose general spatiotemporal constraints  ...  of voxels for which the ᭜ Yamashita et al. ᭜ ᭜ 222 ᭜ ᭜ RPLS Solution for Dynamical Inverse Problems ᭜ ᭜ 223 ᭜ ᭜ RPLS Solution for Dynamical Inverse Problems ᭜ ᭜ 227 ᭜ ᭜ RPLS Solution for Dynamical Inverse  ...  ACKNOWLEDGMENTS This research was supported in part by the Japan Society for the Promotion of Science (JSPS) (fellowship P03059 to A.G.) and by Deutsche Forschungsgemeinschaft (project GA 673/1-1 to A.G  ... 
doi:10.1002/hbm.20000 pmid:15038004 fatcat:xdoakukw7rfrlfoujwz6uqopqq

A data-driven model of the generation of human EEG based on a spatially distributed stochastic wave equation

Andreas Galka, Tohru Ozaki, Hiltrud Muhle, Ulrich Stephani, Michael Siniatchkin
2008 Cognitive Neurodynamics  
Through this step it becomes possible to employ EEG recordings for the purpose of estimating the primary current density vector field, i.e. finding a solution of the inverse problem of EEG generation.  ...  The resulting algorithm for estimating dynamical solutions of the EEG inverse problem is applied to the task of localising the source of an epileptic spike from a clinical EEG data set; for comparison,  ...  The first author is grateful to Matthew Barton and Peter Robinson for useful discussions.  ... 
doi:10.1007/s11571-008-9049-x pmid:19003477 pmcid:PMC2427060 fatcat:dwlzmzy5wrd2zd637pdymysidy

Contextual MEG and EEG Source Estimates Using Spatiotemporal LSTM Networks

Christoph Dinh, John G Samuelsson, Alexander Hunold, Matti S Hämäläinen, Sheraz Khan
2021 Frontiers in Neuroscience  
Here, we use a network of Long Short-Term Memory (LSTM) cells where the input is a sequence of past source estimates and the output is a prediction of the following estimate.  ...  This prediction is then used to correct the estimate. In this study, we applied this technique on noise-normalized minimum norm estimates (MNE).  ...  This assumption ignores the temporal structure of the underlying neural activity that could be used to help reduce the ill-posedness of the inverse problem by constraining the solution space.  ... 
doi:10.3389/fnins.2021.552666 pmid:33767606 pmcid:PMC7985163 fatcat:bcgiequ4jfbdxnjfgvmzt6up3e

A spatiotemporal dynamic distributed solution to the MEG inverse problem

Camilo Lamus, Matti S. Hämäläinen, Simona Temereanca, Emery N. Brown, Patrick L. Purdon
2012 NeuroImage  
Because spatiotemporal dynamics of this kind are central to brain physiology, inverse solutions could be improved by incorporating models of these dynamics.  ...  We develop a dynamic Maximum a Posteriori Expectation-Maximization (dMAP-EM) source localization algorithm for estimation of cortical sources and model parameters based on the Kalman Filter, the Fixed  ...  For the inverse problem, solution of the corresponding forward problem in MEG/EEG, i.e., determining the measured magnetic and electric field at the scalp generated by a given distribution of neuronal  ... 
doi:10.1016/j.neuroimage.2011.11.020 pmid:22155043 pmcid:PMC3432302 fatcat:lz7wamgjuzhc5jp7obsbcvmyga

State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing

Christopher J. Long, Patrick L. Purdon, Simona Temereanca, Neil U. Desai, Matti S. Hämäläinen, Emery N. Brown
2011 Annals of Applied Statistics  
Determining the magnitude and location of neural sources within the brain that are responsible for generating magnetoencephalography (MEG) signals measured on the surface of the head is a challenging problem  ...  In our model, the observation model is derived from the steady-state solution to Maxwell's equations while the latent model representing neural dynamics is given by a random walk process.  ...  We show that two solutions that are naturally suited to this type of dynamic inverse problem are the Kalman filter and the fixed-interval smoother [Kitagawa and Gersch (1996) , Kay (1993) ].  ... 
doi:10.1214/11-aoas483 pmid:22081780 pmcid:PMC3212953 fatcat:4jdil27nhzamda7vburpj37ery

A Spatiotemporal Dynamic Solution to the MEG Inverse Problem: An Empirical Bayes Approach [article]

Camilo Lamus, Matti S. Hämäläinen, Simona Temereanca, Emery N. Brown, Patrick L. Purdon
2016 arXiv   pre-print
Because spatiotemporal dynamics of this kind are central to brain physiology, inverse solutions could be improved by incorporating models of these dynamics.  ...  We develop a dynamic Maximum a Posteriori Expectation-Maximization (dMAP-EM) source localization algorithm for estimation of cortical sources and model parameters based on the Kalman Filter, the Fixed  ...  For the inverse problem, solution of the corresponding forward problem in MEG/EEG, i.e., determining the measured magnetic and electric field at the scalp generated by a given distribution of neuronal  ... 
arXiv:1511.05056v3 fatcat:4k6ioqqhobgnjl2dnj7wlghske

Bayesian inverse methods for spatiotemporal characterization of gastric electrical activity from cutaneous multi-electrode recordings

Alexis B. Allegra, Armen A. Gharibans, Gabriel E. Schamberg, David C. Kunkel, Todd P. Coleman, Seungil Ro
2019 PLoS ONE  
We employ Bayesian inference to solve the ill-posed inverse problem of estimating gastric surface activity from cutaneous recordings.  ...  We utilize a prior distribution on the spatiotemporal activity pertaining to sparsity in the number of wavefronts on the stomach surface, and smooth evolution of these wavefronts across time.  ...  The authors would also like to thank Dr. Hayat Mousa at the Neurogastroenterology and Motility Center, Rady Children's Hospital for her insight and helpful discussions.  ... 
doi:10.1371/journal.pone.0220315 pmid:31609972 pmcid:PMC6791545 fatcat:aca2tdsv7bb3tcsfvqkckwsn6y

Contextual Minimum-Norm Estimates (CMNE): A Deep Learning Method for Source Estimation in Neuronal Networks [article]

Christoph Dinh, John GW Samuelsson, Alexander Hunold, Matti S Hämäläinen, Sheraz Khan
2019 arXiv   pre-print
To evaluate the performance of CMNE, it was tested on simulated and experimental data from human auditory evoked response experiments.  ...  However, neuronal assemblies are heavily interconnected, constraining the temporal evolution of neural activity in space as detected by MEG and EEG.  ...  Recent developments introduce source estimation methods based on more realistic spatiotemporal dynamic models using Kalman filters (Kalman 1960) , which take local cortical interactions considering neuroanatomical  ... 
arXiv:1909.02636v1 fatcat:ff5c55c4snez7j7h52qmxkezja

Efficient algorithms for the regularization of dynamic inverse problems: II. Applications

U Schmitt, A K Louis, C Wolters, M Vauhkonen
2002 Inverse Problems  
In the first part of this paper the notion of dynamic inverse problems was introduced and two procedures, namely STR and STR-C, for the efficient spatiotemporal regularization of such problems were developed  ...  A comparison to a Kalman smoother approach will be given for dynEIT.  ...  by the Leipniz-Prize of the German Research Foundation awarded to Professor A D Friederici, director of the MPI of Cognitive Neuroscience, Leipzig.  ... 
doi:10.1088/0266-5611/18/3/309 fatcat:rsey6z5psjbdzcheq5gqqovgy4

Dynamic Electrical Source Imaging (DESI) of Seizures and Interictal Epileptic Discharges Without Ensemble Averaging

Burak Erem, Damon E. Hyde, Jurriaan M. Peters, Frank H. Duffy, Simon K. Warfield
2017 IEEE Transactions on Medical Imaging  
We propose an algorithm for electrical source imaging of epileptic discharges that takes a datadriven approach to regularizing the dynamics of solutions.  ...  The same approach could be used in the planning of epilepsy surgeries, as a way to localize potentially epileptogenic tissue that should be resected.  ...  We would like to thank Dr. Phillip Pearl, Dr. Joseph Madsen, Sheryl Manganaro, Lixia Gao, and Vinh Huynh for their help with the data.  ... 
doi:10.1109/tmi.2016.2595329 pmid:27479957 pmcid:PMC5217759 fatcat:2q6b45xvajfxzgeev4rz2uocy4

Dynamic physiological modeling for functional diffuse optical tomography

Solomon Gilbert Diamond, Theodore J. Huppert, Ville Kolehmainen, Maria Angela Franceschini, Jari P. Kaipio, Simon R. Arridge, David A. Boas
2006 NeuroImage  
The further improvement with the Kalman filter encourages continued research into dynamic linear modeling of the physiology present in DOT.  ...  Adding physiological modeling with a static estimator significantly improved estimates of the simulated functional response, and further significant improvements were achieved with a dynamic Kalman filter  ...  Brooks, Ph.D. of Northeastern University for reviewing the manuscript and providing insightful feedback.  ... 
doi:10.1016/j.neuroimage.2005.09.016 pmid:16242967 pmcid:PMC2670202 fatcat:gr5u3k6z55flvij5uambewnkjy

A Novel Bayesian Approach for EEG Source Localization

Vangelis P. Oikonomou, Ioannis Kompatsiaris, Vahid Rakhshan
2020 Computational Intelligence and Neuroscience  
We propose a new method for EEG source localization. An efficient solution to this problem requires choosing an appropriate regularization term in order to constraint the original problem.  ...  In order to obtain an efficient algorithm, we use the variational Bayesian (VB) framework which provides us with a tractable iterative algorithm of closed-form equations.  ...  Clearly, the linear observation model [17, 18] , the linear dynamical model (or Kalman Filters) [17, 18] , and the multiple measurement vector (MMV) model [19] make different generative modelling assumptions  ... 
doi:10.1155/2020/8837954 pmid:33178259 pmcid:PMC7647781 fatcat:gubvyhxo25esznums5ndhbmtsy

Improved Localization of Seizure Onset Zones Using Spatiotemporal Constraints and Time-Varying Source Connectivity

Juan D. Martinez-Vargas, Gregor Strobbe, Kristl Vonck, Pieter van Mierlo, German Castellanos-Dominguez
2017 Frontiers in Neuroscience  
In particular, we encode the source nonstationarities in three critical stages of processing: Inverse problem solution, estimation of the time courses extracted from the regions of interest, and connectivity  ...  With the aim to correctly encode all temporal dynamics of the seizure-related neural network, a directed functional connectivity measure is employed to quantify the information flow variations over the  ...  Accordingly, the source imaging methods are employed, which address the EEG inverse problem, to map the acquired neural data into source space information with the aim to localize the epileptic generators  ... 
doi:10.3389/fnins.2017.00156 pmid:28428738 pmcid:PMC5382162 fatcat:vbug3pp4s5ftdbrhdr7nimjabq
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