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1. Fast ℓ1 -regularized EEG source localization using variable projection

   https://doi.org/10.1088/1361-6420/addde4  

   Michael_Solomon, Jack; Anne_Renaut, Rosemary; Chung, Matthias (June 2025, Inverse Problems)

   Electroencephalograms (EEG) are invaluable for treating neurological disorders, however, mapping EEG electrode readings to brain activity requires solving a challenging inverse problem. For time series data, the use of ℓ1 regularization quickly becomes intractable for many solvers, and, despite the reconstruction advantages of ℓ1 regularization, ℓ2-based approaches such as standardized low-resolution brain electromagnetic tomography sLORETA are used in practice. In this work, we formulate EEG source localization as a graphical generalized elastic net inverse problem and present a variable projected augmented Lagrangian algorithm (VPAL) suitable for fast EEG source localization. We prove convergence of this solver for a broad class of separable convex, potentially non-smooth functions subject to linear constraints. Leveraging the efficiency of the proposed VPAL algorithm, we introduce a windowed variation, VPALW, that computes time dynamics in sequence suitable for real-time reconstruction. Our proposed methods are compared to state-of-the-art approaches including sLORETA and other methods for ℓ1-regularized inverse problems. 

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2. Predicting Spatio-Temporal Human Brain Response Using fMRI

   https://doi.org/10.1007/978-3-031-16431-6_32  

   Zhao, Chongyue; Zhan, Liang; Thompson, Paul M; Huang, Heng. (September 2022, Medical Image Computing and Computer Assisted Intervention – MICCAI 2022. Lecture Notes in Computer Science.)

   The transformation and transmission of brain stimuli reflect the dynamical brain activity in space and time. Compared with functional magnetic resonance imaging (fMRI), magneto- or electroencephalography (M/EEG) fast couples to the neural activity through generated magnetic fields. However, the MEG signal is inhomogeneous throughout the whole brain, which is affected by the signal-to-noise ratio, the sensors’ location and distance. Current non-invasive neuroimaging modalities such as fMRI and M/EEG excel high resolution in space or time but not in both. To solve the main limitations of current technique for brain activity recording, we propose a novel recurrent memory optimization approach to predict the internal behavioral states in space and time. The proposed method uses Optimal Polynomial Projections to capture the long temporal history with robust online compression. The training process takes the pairs of fMRI and MEG data as inputs and predicts the recurrent brain states through the Siamese network. In the testing process, the framework only uses fMRI data to generate the corresponding neural response in space and time. The experimental results with Human connectome project (HCP) show that the predicted signal could reflect the neural activity with high spatial resolution as fMRI and high temporal resolution as MEG signal. The experimental results demonstrate for the first time that the proposed method is able to predict the brain response in both milliseconds and millimeters using only fMRI signal. 

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3. Development of an Adaptive Artifact Subspace Reconstruction Based on Hebbian/Anti-Hebbian Learning Networks for Enhancing BCI Performance

   https://doi.org/10.1109/TNNLS.2022.3174528  

   Tsai, Bo-Yu; Diddi, Sandeep Vara; Ko, Li-Wei; Wang, Shuu-Jiun; Chang, Chi-Yuan; Jung, Tzyy-Ping (June 2022, IEEE Transactions on Neural Networks and Learning Systems)

   Brain-computer interface (BCI) actively translates the brain signals into executable actions by establishing direct communication between the human brain and external devices. Recording brain activity through electroencephalography (EEG) is generally contaminated with both physiological and nonphysiological artifacts, which significantly hinders the BCI performance. Artifact subspace reconstruction (ASR) is a well-known statistical technique that automatically removes artifact components by determining the rejection threshold based on the initial reference EEG segment in multichannel EEG recordings. In real-world applications, the fixed threshold may limit the efficacy of the artifact correction, especially when the quality of the reference data is poor. This study proposes an adaptive online ASR technique by integrating the Hebbian/anti-Hebbian neural networks into the ASR algorithm, namely, principle subspace projection ASR (PSP-ASR) and principal subspace whitening ASR (PSW-ASR) that segmentwise self-organize the artifact subspace by updating the synaptic weights according to the Hebbian and anti-Hebbian learning rules. The effectiveness of the proposed algorithm is compared to the conventional ASR approaches on benchmark EEG dataset and three BCI frameworks, including steady-state visual evoked potential (SSVEP), rapid serial visual presentation (RSVP), and motor imagery (MI) by evaluating the root-mean-square error (RMSE), the signal-to-noise ratio (SNR), the Pearson correlation, and classification accuracy. The results demonstrated that the PSW-ASR algorithm effectively removed the EEG artifacts and retained the activity-specific brain signals compared to the PSP-ASR, standard ASR (Init-ASR), and moving-window ASR (MW-ASR) methods, thereby enhancing the SSVEP, RSVP, and MI BCI performances. Finally, our empirical results from the PSW-ASR algorithm suggested the choice of an aggressive cutoff range of c = 1-10 for activity-specific BCI applications and a moderate range of for the benchmark dataset and general BCI applications. 

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4. Revealing Continuous Brain Dynamical Organization with Multimodal Graph Transformer

   https://doi.org/10.1007/978-3-031-16431-6_33  

   Zhao, Chongyue; Zhan, Liang; Thompson, Paul M.; Huang, Heng. (September 2022, Medical Image Computing and Computer Assisted Intervention – MICCAI 2022. Lecture Notes in Computer Science.)

   Brain large-scale dynamics is constrained by the heterogeneity of intrinsic anatomical substrate. Little is known how the spatiotemporal dynamics adapt for the heterogeneous structural connectivity (SC). Modern neuroimaging modalities make it possible to study the intrinsic brain activity at the scale of seconds to minutes. Diffusion magnetic resonance imaging (dMRI) and functional MRI reveals the large-scale SC across different brain regions. Electrophysiological methods (i.e. MEG/EEG) provide direct measures of neural activity and exhibits complex neurobiological temporal dynamics which could not be solved by fMRI. However, most of existing multimodal analytical methods collapse the brain measurements either in space or time domain and fail to capture the spatio-temporal circuit dynamics. In this paper, we propose a novel spatio-temporal graph Transformer model to integrate the structural and functional connectivity in both spatial and temporal domain. The proposed method learns the heterogeneous node and graph representation via contrastive learning and multi-head attention based graph Transformer using multimodal brain data (i.e. fMRI, MRI, MEG and behavior performance). The proposed contrastive graph Transformer representation model incorporates the heterogeneity map constrained by T1-to-T2-weighted (T1w/T2w) to improve the model fit to structurefunction interactions. The experimental results with multimodal resting state brain measurements demonstrate the proposed method could highlight the local properties of large-scale brain spatio-temporal dynamics and capture the dependence strength between functional connectivity and behaviors. In summary, the proposed method enables the complex brain dynamics explanation for different modal variants. 

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5. Hypergraph reconstruction from dynamics

   https://doi.org/10.1038/s41467-025-57664-2  

   Delabays, Robin; De_Pasquale, Giulia; Dörfler, Florian; Zhang, Yuanzhao (December 2025, Nature Communications)

   A plethora of methods have been developed in the past two decades to infer the underlying network structure of an interconnected system from its collective dynamics. However, methods capable of inferring nonpairwise interactions are only starting to appear. Here, we develop an inference algorithm based on sparse identification of nonlinear dynamics (SINDy) to reconstruct hypergraphs and simplicial complexes from time-series data. Our model-free method does not require information about node dynamics or coupling functions, making it applicable to complex systems that do not have a reliable mathematical description. We first benchmark the new method on synthetic data generated from Kuramoto and Lorenz dynamics. We then use it to infer the effective connectivity in the brain from resting-state EEG data, which reveals significant contributions from non-pairwise interactions in shaping the macroscopic brain dynamics. 

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