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We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and…

Quantitative Methods · Quantitative Biology 2017-05-09 Alberto Sorrentino , Michele Piana

Analyzing and reconstructing visual stimuli from brain signals effectively advances the understanding of human visual system. However, the EEG signals are complex and contain significant noise. This leads to substantial limitations in…

Computer Vision and Pattern Recognition · Computer Science 2025-04-24 Honghao Fu , Zhiqi Shen , Jing Jih Chin , Hao Wang

In recent years, multiple noninvasive imaging modalities have been used to develop a better understanding of the human brain functionality, including positron emission tomography, single-photon emission computed tomography, and functional…

Signal Processing · Electrical Eng. & Systems 2019-10-18 Shiva Asadzadeh , Tohid Yousefi Rezaii , Soosan Beheshti , Azra Delpak , Saeed Meshgini

MEG and EEG are noninvasive functional neuroimaging techniques that provide recordings of brain activity with high temporal resolution, and thus provide a unique window to study fast time-scale neural dynamics in humans. However, the…

Applications · Statistics 2015-11-13 Camilo Lamus , Matti S. Hamalainen , Emery N. Brown , Patrick L. Purdon

Electroencephalography (EEG) is widely used to study human brain dynamics, yet its quantitative information capacity remains unclear. Here, we combine information theory and synthetic forward modeling to estimate the mutual information…

Information Theory · Computer Science 2025-10-22 Ishir Rao

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…

Computational Engineering, Finance, and Science · Computer Science 2019-08-30 Kostiantyn Maksymenko , Maureen Clerc , Théodore Papadopoulo

The reconstruction of 3D objects from brain signals has gained significant attention in brain-computer interface (BCI) research. Current research predominantly utilizes functional magnetic resonance imaging (fMRI) for 3D reconstruction…

Graphics · Computer Science 2025-05-06 Xia Deng , Shen Chen , Jiale Zhou , Lei Li

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

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…

Signal Processing · Electrical Eng. & Systems 2022-10-28 Teja Mannepalli , Aurobinda Routray

Reconstructing visual stimuli from non-invasive electroencephalography (EEG) remains challenging due to its low spatial resolution and high noise, particularly under realistic low-density electrode configurations. To address this, we…

Computer Vision and Pattern Recognition · Computer Science 2026-04-10 Emanuele Balloni , Emanuele Frontoni , Chiara Matti , Marina Paolanti , Roberto Pierdicca , Emiliano Santarnecchi

Electroencephalography (EEG) has become one of the key modalities underpinning brain-computer interfaces (BCIs) due to its high temporal resolution, rapid responsiveness, non-invasiveness, low cost, and portability. However, EEG signals are…

Neurons and Cognition · Quantitative Biology 2026-04-17 Yihang Dong , Changhong Jing , Shuqiang Wang

In this paper we propose spatial filters for a linear regression model which are based on the minimum-variance pseudo-unbiased reduced-rank estimation (MV-PURE) framework. As a sample application, we consider the problem of reconstruction…

Signal Processing · Electrical Eng. & Systems 2024-08-02 Tomasz Piotrowski , Jan Nikadon , David Gutierrez

Brain responses related to working memory originate from distinct brain areas and oscillate at different frequencies. EEG signals with high temporal correlation can effectively capture these responses. Therefore, estimating the functional…

Machine Learning · Computer Science 2024-05-01 Harshini Gangapuram , Vidya Manian

Current non-invasive neuroimaging techniques trade off between spatial resolution and temporal resolution. While magnetoencephalography (MEG) can capture rapid neural dynamics and functional magnetic resonance imaging (fMRI) can spatially…

Neurons and Cognition · Quantitative Biology 2025-10-13 Beige Jerry Jin , Leila Wehbe

In this paper, we analyze electroencephalograms (EEG) which are recordings of brain electrical activity. We develop new clustering methods for identifying synchronized brain regions, where the EEGs show similar oscillations or waveforms…

Methodology · Statistics 2020-07-29 Tianbo Chen , Ying Sun , Carolina Euan , Hernando Ombao

This work considers the optimization of electrode positions in head imaging by electrical impedance tomography. The study is motivated by maximizing the sensitivity of electrode measurements to conductivity changes when monitoring the…

Numerical Analysis · Mathematics 2023-12-19 N. Hyvönen , A. Jääskeläinen , R. Maity , A. Vavilov

Accurate electroencephalography (EEG) and magnetoencephalography (MEG) source localization and reconstruction are essential for understanding brain function, yet remain challenging because the underlying EEG/MEG inverse problem is…

Optimization and Control · Mathematics 2026-04-29 Julia Jurkowska , Joanna Dreszer , Monika Lewandowska , Krzysztof Tołpa , Tomasz Piotrowski

Seeing is believing, however, the underlying mechanism of how human visual perceptions are intertwined with our cognitions is still a mystery. Thanks to the recent advances in both neuroscience and artificial intelligence, we have been able…

Image and Video Processing · Electrical Eng. & Systems 2023-08-17 Yu-Ting Lan , Kan Ren , Yansen Wang , Wei-Long Zheng , Dongsheng Li , Bao-Liang Lu , Lili Qiu

In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity. For standard Lasso theory to hold, the regularization parameter should be proportional to the noise level, yet the latter is generally unknown in…

Machine Learning · Statistics 2017-10-19 Mathurin Massias , Olivier Fercoq , Alexandre Gramfort , Joseph Salmon

Speech enhancement is widely used as a front-end to improve the speech quality in many audio systems, while it is hard to extract the target speech in multi-talker conditions without prior information on the speaker identity. It was shown…

Audio and Speech Processing · Electrical Eng. & Systems 2024-06-26 Jie Zhang , Qing-Tian Xu , Zhen-Hua Ling , Haizhou Li