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## Filters

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

2004
*
NeuroImage
*

We present

doi:10.1016/j.neuroimage.2004.02.022
pmid:15488394
fatcat:vecvm5mzwzhzhd2nyhij7h2ha4
*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. ...##
###
GARCH modelling of covariance in dynamical estimation of inverse solutions

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 ...

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

2004
*
Human Brain Mapping
*

In

doi:10.1002/hbm.20000
pmid:15038004
fatcat:xdoakukw7rfrlfoujwz6uqopqq
*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 ...##
###
A data-driven model of the generation of human EEG based on a spatially distributed stochastic wave equation

2008
*
Cognitive Neurodynamics
*

Through this step it becomes possible

doi:10.1007/s11571-008-9049-x
pmid:19003477
pmcid:PMC2427060
fatcat:dwlzmzy5wrd2zd637pdymysidy
*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. ...##
###
Contextual MEG and EEG Source Estimates Using Spatiotemporal LSTM Networks

2021
*
Frontiers in Neuroscience
*

Here, we

doi:10.3389/fnins.2021.552666
pmid:33767606
pmcid:PMC7985163
fatcat:bcgiequ4jfbdxnjfgvmzt6up3e
*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. ...##
###
A spatiotemporal dynamic distributed solution to the MEG inverse problem

2012
*
NeuroImage
*

Because

doi:10.1016/j.neuroimage.2011.11.020
pmid:22155043
pmcid:PMC3432302
fatcat:lz7wamgjuzhc5jp7obsbcvmyga
*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 ...##
###
State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing

2011
*
Annals of Applied Statistics
*

Determining

doi:10.1214/11-aoas483
pmid:22081780
pmcid:PMC3212953
fatcat:4jdil27nhzamda7vburpj37ery
*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) ]. ...##
###
A Spatiotemporal Dynamic Solution to the MEG Inverse Problem: An Empirical Bayes Approach
[article]

2016
*
arXiv
*
pre-print

Because

arXiv:1511.05056v3
fatcat:4k6ioqqhobgnjl2dnj7wlghske
*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 ...##
###
Bayesian inverse methods for spatiotemporal characterization of gastric electrical activity from cutaneous multi-electrode recordings

2019
*
PLoS ONE
*

We employ Bayesian inference

doi:10.1371/journal.pone.0220315
pmid:31609972
pmcid:PMC6791545
fatcat:aca2tdsv7bb3tcsfvqkckwsn6y
*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. ...##
###
Contextual Minimum-Norm Estimates (CMNE): A Deep Learning Method for Source Estimation in Neuronal Networks
[article]

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 ...

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

2002
*
Inverse Problems
*

In

doi:10.1088/0266-5611/18/3/309
fatcat:rsey6z5psjbdzcheq5gqqovgy4
*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. ...##
###
Dynamic Electrical Source Imaging (DESI) of Seizures and Interictal Epileptic Discharges Without Ensemble Averaging

2017
*
IEEE Transactions on Medical Imaging
*

We propose an algorithm for electrical source imaging

doi:10.1109/tmi.2016.2595329
pmid:27479957
pmcid:PMC5217759
fatcat:2q6b45xvajfxzgeev4rz2uocy4
*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. ...##
###
Dynamic physiological modeling for functional diffuse optical tomography

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. ...

##
###
A Novel Bayesian Approach for EEG Source Localization

2020
*
Computational Intelligence and Neuroscience
*

We propose

doi:10.1155/2020/8837954
pmid:33178259
pmcid:PMC7647781
fatcat:gubvyhxo25esznums5ndhbmtsy
*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 ...##
###
Improved Localization of Seizure Onset Zones Using Spatiotemporal Constraints and Time-Varying Source Connectivity

2017
*
Frontiers in Neuroscience
*

In particular, we encode

doi:10.3389/fnins.2017.00156
pmid:28428738
pmcid:PMC5382162
fatcat:vbug3pp4s5ftdbrhdr7nimjabq
*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*...
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