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We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…

Numerical Analysis · Mathematics 2025-12-05 Martin Burger , Ole Løseth Elvetun , Bjørn Fredrik Nielsen

Human visual reconstruction aims to reconstruct fine-grained visual stimuli based on subject-provided descriptions and corresponding neural signals. As a widely adopted modality, Electroencephalography (EEG) captures rich visual cognition…

Computer Vision and Pattern Recognition · Computer Science 2026-03-23 Zhijian Gong , Tianren Yao , Wenjia Dong , Xueyuan Xu

Electroencephalogram (EEG) is a common tool used to understand brain activities. The data are typically obtained by placing electrodes at the surface of the scalp and recording the oscillations of currents passing through the electrodes.…

Signal Processing · Electrical Eng. & Systems 2021-02-19 Eddy Kwessi , Lloyd Edwards

We present an algorithm for focusing inversion of electrical resistivity tomography (ERT) data. ERT is a typical example of ill-posed problem. Regularization is the most common way to face this kind of problems; it basically consists in…

Geophysics · Physics 2007-05-23 G. Pagliara , G. Vignoli

EEG based brain state decoding has numerous applications. State of the art decoding is based on processing of the multivariate sensor space signal, however evidence is mounting that EEG source reconstruction can assist decoding. EEG source…

Neurons and Cognition · Quantitative Biology 2017-04-20 Rasmus S. Andersen , Anders U. Eliasen , Nicolai Pedersen , Michael Riis Andersen , Sofie Therese Hansen , Lars Kai Hansen

Unsupervised audio-visual source localization aims at localizing visible sound sources in a video without relying on ground-truth localization for training. Previous works often seek high audio-visual similarities for likely positive…

Computer Vision and Pattern Recognition · Computer Science 2022-03-30 Shentong Mo , Pedro Morgado

In magnetoencephalography (MEG) the conventional approach to source reconstruction is to solve the underdetermined inverse problem independently over time and space. Here we present how the conventional approach can be extended by…

The variable projection (VarPro) method is an efficient method to solve separable nonlinear least squares problems. In this paper, we propose a modified VarPro for large-scale separable nonlinear inverse problems that promotes…

Numerical Analysis · Mathematics 2021-06-01 Malena Espanol , Mirjeta Pasha

Electroencephalography (EEG) signals reflect activities on certain brain areas. Effective classification of time-varying EEG signals is still challenging. First, EEG signal processing and feature engineering are time-consuming and highly…

Human-Computer Interaction · Computer Science 2019-08-27 Xiang Zhang , Lina Yao , Xianzhi Wang , Wenjie Zhang , Shuai Zhang , Yunhao Liu

We describe a novel method for dynamic estimation of multi-dipole states from Magneto/Electro-encephalography (M/EEG) time series. The new approach builds on the recent development of particle filters for M/EEG; these algorithms…

Numerical Analysis · Mathematics 2016-03-18 Valentina Vivaldi , Alberto Sorrentino

Chronic neck pain is a leading cause of disability worldwide, and current treatment selection remains largely trial and error. We present a machine learning framework that uses electroencephalography to predict treatment efficacy in…

Quantitative Methods · Quantitative Biology 2026-05-19 Xiru Wang , Aiden Li , Hongzhao Tan , Stevie Foglia , Aimee Nelson , Zhen Gao

Electroencephalography (EEG) is a non-invasive technique for recording brain activity, widely used in brain-computer interfaces, clinic, and healthcare. Traditional EEG deep models typically focus on specific dataset and task, limiting…

Signal Processing · Electrical Eng. & Systems 2025-09-03 Ang Li , Zikai Wang , Liuyin Yang , Zhenyu Wang , Tianheng Xu , Honglin Hu , Marc M. Van Hulle

This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedance tomography (EIT), which is known to be a nonlinear and…

Numerical Analysis · Mathematics 2019-08-01 Jin Keun Seo , Kang Cheol Kim , Ariungerel Jargal , Kyounghun Lee , Bastian Harrach

Electroencephalography (EEG) is a widely used non-invasive technique for measuring brain activity in brain-computer interface (BCI) applications. Supervised EEG decoding models often struggle to generalize across tasks, subjects, and…

Artificial Intelligence · Computer Science 2026-05-29 Ayse Betul Yuce , Sebastian Stober

Electromagnetic source imaging (ESI) requires solving a highly ill-posed inverse problem. To seek a unique solution, traditional ESI methods impose various forms of priors that may not accurately reflect the actual source properties, which…

Image and Video Processing · Electrical Eng. & Systems 2022-07-14 Gexin Huang , Jiawen Liang , Ke Liu , Chang Cai , ZhengHui Gu , Feifei Qi , Yuan Qing Li , Zhu Liang Yu , Wei Wu

Electroencephalogram (EEG) classification plays a key role in medical diagnosis and brain-computer interfaces, but remains challenging due to low signal-to-noise ratios and high inter-subject variability. As a result, many existing…

Machine Learning · Computer Science 2026-05-18 Ahmad Bdeir , Johannes Burchert , Tom Hanika , Lars Schmidt-Thieme , Niels Landwehr

Machine learning (ML)-based analysis of electroencephalograms (EEGs) is playing an important role in advancing neurological care. However, the difficulties in automatically extracting useful metadata from clinical records hinder the…

Computation and Language · Computer Science 2021-09-14 Samarth Rawal , Yogatheesan Varatharajah

Knowing the correct skull conductivity is crucial for the accuracy of EEG source imaging, but unfortunately, its true value, which is inter- and intra-individually varying, is difficult to determine. In this paper, we propose a statistical…

Medical Physics · Physics 2020-09-07 Ville Rimpiläinen , Alexandra Koulouri , Felix Lucka , Jari P Kaipio , Carsten H Wolters

This paper presents a regularization technique incorporating a non-convex and non-smooth term, $\ell_{1}^{2}-\eta\ell_{2}^{2}$, with parameters $0<\eta\leq 1$ designed to address ill-posed linear problems that yield sparse solutions. We…

Optimization and Control · Mathematics 2025-06-16 Long Li , Liang Ding

Electroencephalography (EEG) analysis is an important domain in the realm of Brain-Computer Interface (BCI) research. To ensure BCI devices are capable of providing practical applications in the real world, brain signal processing…

Signal Processing · Electrical Eng. & Systems 2024-08-08 Teng Liang , Andrews Damoah