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Related papers: Inverse Modeling for MEG/EEG data

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We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic…

Analysis of PDEs · Mathematics 2017-10-25 Youjun Deng , Hongyu Liu , Gunther Uhlmann

Bayesian modeling and analysis of the MEG and EEG modalities provide a flexible framework for introducing prior information complementary to the measured data. This prior information is often qualitative in nature, making the translation of…

Mathematical Physics · Physics 2008-11-20 Daniela Calvetti , Harri Hakula , Sampsa Pursiainen , Erkki Somersalo

State-space models are widely employed across various research disciplines to study unobserved dynamics. Conventional estimation techniques, such as Kalman filtering and expectation maximisation, offer valuable insights but incur high…

Computation · Statistics 2023-11-28 Jose M. Sanchez-Bornot , Roberto C. Sotero , Scott Kelso , Damien Coyle

In this article, normal inverse Gaussian (NIG) autoregressive model is introduced. The parameters of the model are estimated using Expectation Maximization (EM) algorithm. The efficacy of the EM algorithm is shown using simulated and real…

Methodology · Statistics 2021-07-16 Monika Singh Dhull , Arun Kumar

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…

Machine Learning · Computer Science 2025-08-05 Hyungjin Chung , Jeongsol Kim , Jong Chul Ye

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…

Numerical Analysis · Mathematics 2015-06-19 Julianne Chung , Matthias Chung

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…

Applications · Statistics 2014-03-20 Alberto Sorrentino , Gianvittorio Luria , Riccardo Aramini

These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…

Probability · Mathematics 2015-07-03 Masoumeh Dashti , Andrew M. Stuart

The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…

Optimization and Control · Mathematics 2025-06-24 Clemens Kirisits , Bochra Mejri , Sergei Pereverzev , Otmar Scherzer , Cong Shi

This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connecting vertices. We focus on the inverse problem of recovering…

Analysis of PDEs · Mathematics 2026-03-30 David Bolin , Wenwen Li , Daniel Sanz-Alonso

We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such…

Numerical Analysis · Mathematics 2021-02-09 Harbir Antil , Howard C Elman , Akwum Onwunta , Deepanshu Verma

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…

Machine Learning · Computer Science 2020-08-24 Francesco Tonolini , Jack Radford , Alex Turpin , Daniele Faccio , Roderick Murray-Smith

Brain source imaging is an important method for noninvasively characterizing brain activity using Electroencephalogram (EEG) or Magnetoencephalography (MEG) recordings. Traditional EEG/MEG Source Imaging (ESI) methods usually assume that…

Applications · Statistics 2019-06-07 Feng Liu , Li Wang , Yifei Lou , Rencang Li , Patrick Purdon

Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…

Numerical Analysis · Mathematics 2020-06-09 Markus Haltmeier , Linh V. Nguyen

The reconstruction of the structure of biological tissue using electromyographic data is a non-invasive imaging method with diverse medical applications. Mathematically, this process is an inverse problem. Furthermore, electromyographic…

Numerical Analysis · Mathematics 2021-05-26 Anna Rörich , Tim A. Werthmann , Dominik Göddeke , Lars Grasedyck

Reconstructing images using brain signals of imagined visuals may provide an augmented vision to the disabled, leading to the advancement of Brain-Computer Interface (BCI) technology. The recent progress in deep learning has boosted the…

Human-Computer Interaction · Computer Science 2023-03-21 Prajwal Singh , Pankaj Pandey , Krishna Miyapuram , Shanmuganathan Raman

To handle with inverse problems, two probabilistic approaches have been proposed: the maximum entropy on the mean (MEM) and the Bayesian estimation (BAYES). The main object of this presentation is to compare these two approaches which are…

Data Analysis, Statistics and Probability · Physics 2007-05-23 A. Mohammad-Djafari

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

Machine Learning · Statistics 2024-05-28 Sharmila Karumuri , Ilias Bilionis

The wavelet Maximum Entropy on the Mean (wMEM) approach to the MEG inverse problem is revisited and extended to infer brain activity from full space-time data. The resulting dimensionality increase is tackled using a collection of…

Machine Learning · Statistics 2018-07-25 Marie-Christine Roubaud , Jean-Marc Lina , Julie Carrier , B Torrésani

The MEG inverse problem refers to the reconstruction of the neural activity of the brain from magnetoencephalography (MEG) measurements. We propose a two-way regularization (TWR) method to solve the MEG inverse problem under the assumptions…

Applications · Statistics 2012-10-01 Tian Siva Tian , Jianhua Z. Huang , Haipeng Shen , Zhimin Li