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We present a theoretical framework for analyzing spatial sampling of fields in three-dimensional space. The framework bridges Shannon's sampling and information theory to Bayesian probabilistic inference and experimental design. Based on…
Electromagnetic medical imaging in the microwave regime is a hard problem notorious for 1) instability 2) under-determinism. This two-pronged problem is tackled with a two-pronged solution that uses double compression to maximally utilizing…
Electroencephalography (EEG) is a method to record the electrical signals in the brain. Recognizing the EEG patterns in the sleeping brain gives insights into the understanding of sleeping disorders. The dataset under consideration contains…
Source localization using EEG is important in diagnosing various physiological and psychiatric diseases related to the brain. The high temporal resolution of EEG helps medical professionals assess the internal physiology of the brain in a…
Neural networks have become a powerful tool as surrogate models to provide numerical solutions for scientific problems with increased computational efficiency. This efficiency can be advantageous for numerically challenging problems where…
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…
This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source…
This paper proposes a determined blind source separation method using Bayesian non-parametric modelling of sources. Conventionally source signals are separated from a given set of mixture signals by modelling them using non-negative matrix…
Signals recorded from neurons with extracellular planar sensors have a wide range of waveforms and amplitudes. This variety is a result of different physical conditions affecting the ion currents through a cellular membrane. The…
Transfer learning makes use of data or knowledge in one problem to help solve a different, yet related, problem. It is particularly useful in brain-computer interfaces (BCIs), for coping with variations among different subjects and/or…
Electroencephalography (EEG) analysis stands at the forefront of neuroscience and artificial intelligence research, where foundation models are reshaping the traditional EEG analysis paradigm by leveraging their powerful representational…
EDIT: A revised version of this article has been published in the SIAM Journal on Scientific Computing, see https://epubs.siam.org/doi/full/10.1137/23M1582874. In the revised version, the name of the approach was changed from "localized…
The electroencephalography (EEG) forward problem, the computation of the electric potential generated by a known electric current source configuration in the brain, is a key step of EEG source analysis. In this problem, it is often desired…
Continuous electroencephalography (EEG) is routinely used in neurocritical care to monitor seizures and other harmful brain activity, including rhythmic and periodic patterns that are clinically significant. Although deep learning methods…
It is a principal open question whether noninvasive imaging methods in humans can decode information encoded at a spatial scale as fine as the basic functional unit of cortex: cortical columns. We addressed this question in five…
Localizing the sources of electrical activity in the brain from Electroencephalographic (EEG) data is an important tool for non-invasive study of brain dynamics. Generally, the source localization process involves a high-dimensional inverse…
Current foundation models for electroencephalography (EEG) rely on architectures adapted from computer vision or natural language processing, typically treating neural signals as pixel grids or token sequences. This approach overlooks that…
Electroencephalography (EEG) classification techniques have been widely studied for human behavior and emotion recognition tasks. But it is still a challenging issue since the data may vary from subject to subject, may change over time for…
In this paper, we present a robust version of the well-known exact low-resolution electromagnetic tomography (eLORETA) technique, named ReLORETA, to localize brain sources in the presence of different forward model uncertainties. Methods:…
Electroencephalography provides a non-invasive window into brain activity, offering valuable insights for neurological research, brain-computer interfaces, and clinical diagnostics. However, the development of robust machine learning models…