# EMAG: Differentiable 4D Gaussian Mixture Splatting for EEG Spatial Super-Resolution

arXiv: https://arxiv.org/abs/2605.29731 · HTML: https://mlsanity.com/paper/2605.29731/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [4D-Rotor Gaussian Splatting: Towards Efficient Novel View Synthesis for Dynamic Scenes](https://mlsanity.com/paper/2402.03307/) (2024)
- [Generative AI Enables EEG Super-Resolution via Spatio-Temporal Adaptive Diffusion Learning](https://mlsanity.com/paper/2407.03089/) (2024)
- [Deep EEG Super-Resolution: Upsampling EEG Spatial Resolution with Generative Adversarial Networks](https://mlsanity.com/paper/2502.08803/) (2025)
- [sasdim: self-adaptive noise scaling diffusion model for spatial time series imputation](https://mlsanity.com/paper/2309.01988/) (2023)
- [EEG Channel Interpolation Using Deep Encoder-decoder Netwoks](https://mlsanity.com/paper/2009.12244/) (2020)
- [Self-attention-based Diffusion Model for Time-series Imputation in Partial Blackout Scenarios](https://mlsanity.com/paper/2503.01737/) (2025)
- [Step-Aware Residual-Guided Diffusion for EEG Spatial Super-Resolution](https://mlsanity.com/paper/2510.19166/) (2025)
- [RDPI: A Refine Diffusion Probability Generation Method for Spatiotemporal Data Imputation](https://mlsanity.com/paper/2412.12642/) (2024)
- [Electromagnetic Source Imaging via a Data-Synthesis-Based Convolutional Encoder-Decoder Network](https://mlsanity.com/paper/2010.12876/) (2020)
- [Neural Brain Fields: A NeRF-Inspired Approach for Generating Nonexistent EEG Electrodes](https://mlsanity.com/paper/2601.00012/) (2025)

## Abstract (arXiv)

High-density electroencephalography (HD-EEG) enables fine-grained measurement of cortical activity but requires expensive hardware and lengthy setup times, limiting its clinical and research accessibility. We propose EMAG (EEG Mixture of Anisotropic Gaussians), a differentiable framework that reconstructs HD-EEG signals from a sparse subset of low-density (LD) electrodes by representing brain electrical sources as a mixture of anisotropic 4D space-time Gaussians. EMAG places a mixture of multiple Gaussians at each point of a spherical brain grid, each parameterized by a full 4 x 4 precision matrix, enabling anisotropic spatial spreads and explicit coupling between spatial and temporal dimensions. The forward model renders scalp EEG via differentiable Gaussian field contributions at electrode locations, enabling end-to-end training without explicit source localization supervision. We evaluate EMAG on three public EEG benchmarks (Localize-MI, SEED, and SEED-IV) at super-resolution factors of 2x through 8/16x. EMAG outperforms the current state-of-the-art EEG super-resolution method at most super-resolution factors on three standard benchmarks (Localize-MI, SEED, SEED-IV). The explicit Gaussian parameterization further enables direct visualization and interpretability of learned brain source configurations, potentially opening avenues for clinical and neuroscientific applications, such as source localization or biomarker discovery.