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This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…
Non-invasive electrophysiology lacks methods that accurately reconstruct whole-brain spatiotemporal dynamics while incorporating individual cortical geometry, leaving current electroencephalography and magnetoencephalography source imaging…
Source localization in EEG represents a high dimensional inverse problem, which is severely ill-posed by nature. Fortunately, sparsity constraints have come into rescue as it helps solving the ill-posed problems when the signal is sparse.…
Foundation models pre-trained through masked reconstruction on large-scale EEG data have emerged as a promising paradigm for learning generalizable neural representations across diverse brain-computer interface applications. However, a…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
In the past five years, the use of generative and foundational AI systems has greatly improved the decoding of brain activity. Visual perception, in particular, can now be decoded from functional Magnetic Resonance Imaging (fMRI) with…
We propose a Bayesian approach to the problem of multi-reference alignment -- the recovery of signals from noisy, randomly shifted observations. While existing frequentist methods accurately recover the signal at arbitrarily low…
Deep learning is increasingly moving towards a transfer learning paradigm whereby large foundation models are fine-tuned on downstream tasks, starting from an initialization learned on the source task. But an initialization contains…
Our ability to extract the maximal amount of information from future observations at gigahertz frequencies depends on our ability to separate the underlying cosmic microwave background (CMB) from galactic and extragalactic foregrounds. We…
Analysis of brain imaging scans is critical to understanding the way the human brain functions, which can be leveraged to treat injuries and conditions that affect the quality of life for a significant portion of the human population. In…
EEG foundation models are typically pretrained on narrow-source clinical archives and evaluated on benchmarks from the same ecosystem, leaving unclear whether representations encode neural physiology or recording-distribution artifacts. We…
Markov chain Monte Carlo (MCMC) methods form one of the algorithmic foundations of Bayesian inverse problems. The recent development of likelihood-informed subspace (LIS) methods offers a viable route to designing efficient MCMC methods for…
Reconstructing lens potentials and lensed sources can easily become an underconstrained problem, even when the degrees of freedom are low, due to degeneracies, particularly when potential perturbations superimposed on a smooth lens are…
Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivity of the different head tissues. Conductivity values are subject dependent, so non-invasive methods for…
We develop a new methodology for determining the location and dynamics of brain activity from combined magnetoencephalography (MEG) and electroencephalography (EEG) data. The resulting inverse problem is ill-posed and is one of the most…
Two techniques are proposed to alleviate the computational burden of MUltiple SIgnal Classification (MUSIC) algorithm applied to Electroencephalogram (EEG) source localization. A significant reduction was achieved by parsing the cortex…
Bayesian inference methods have been widely applied in inverse problems, {largely due to their ability to characterize the uncertainty associated with the estimation results.} {In the Bayesian framework} the prior distribution of the…
Reconstructing brain sources is a fundamental challenge in neuroscience, crucial for understanding brain function and dysfunction. Electroencephalography (EEG) signals have a high temporal resolution. However, identifying the correct…
Noninvasive reconstruction of cardiac electrical activity from surface electrocardiograms (ECG) involves solving an ill-posed inverse problem. Cardiac electrophysiological (EP) models have been used as important a priori knowledge to…
EEG foundation models aim to learn reusable representations across heterogeneous paradigms, yet existing approaches often use uniform adaptation mechanisms and are typically reported under separate downstream fine-tuning protocols. In this…