Related papers: Inverse Modeling for MEG/EEG data
Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion…
Electroencephalography (EEG) is a tool that allows us to analyze brain activity with high temporal resolution. These measures, combined with deep learning and digital signal processing, are widely used in neurological disorder detection and…
Neuroimaging techniques have shown to be useful when studying the brain's activity. This paper uses Magnetoencephalography (MEG) data, provided by the Human Connectome Project (HCP), in combination with various deep artificial neural…
Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…
Various research initiatives try to utilize the operational principles of organisms and brains to develop alternative, biologically inspired computing paradigms and artificial cognitive systems. This paper reviews key features of the…
Timely diagnosis is important for saving the life of epileptic patients. In past few years, a lot of treatments are available for epilepsy. These treatments require use of anti-seizure drugs but are not effective in controlling frequency of…
Can regularization terms in the training of invertible neural networks lead to known Bayesian point estimators in reconstruction? Invertible networks are attractive for inverse problems due to their inherent stability and interpretability.…
Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models…
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
Electroencephalography (EEG) is an invaluable tool in neuroscience, offering insights into brain activity with high temporal resolution. Recent advancements in machine learning and generative modeling have catalyzed the application of EEG…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
The M/EEG inverse problem is ill-posed. Thus additional hypotheses are needed to constrain the solution space. In this work, we consider that brain activity which generates an M/EEG signal is a connected cortical region. We study the case…
Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically…
We investigate the weighted Group Lasso formulation for the static inverse electroencephalography (EEG) problem, aiming at reconstructing the unknown underlying neuronal sources from voltage measurements on the scalp. By modelling the three…
We propose a model for time series taking values on a Riemannian manifold and fit it to time series of covariance matrices derived from EEG data for patients suffering from epilepsy. The aim of the study is two-fold: to develop a model with…
In this article, the solution of a statistical inverse problem $M = AU+\mathcal{E}$ by the Bayesian approach is studied where $U$ is a function on the unit circle $\mathbb{T}$, i.e., a periodic signal. The mapping $A$ is a smoothing linear…
The human brain receives complex inputs when performing cognitive tasks, which range from external inputs via the senses to internal inputs from other brain regions. However, the explicit inputs to the brain during a cognitive task remain…
Exponential random graph models (ERGMs) are very flexible for modeling network formation but pose difficult estimation challenges due to their intractable normalizing constant. Existing methods, such as MCMC-MLE, rely on sequential…
We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…