# Enhancing Brain Source Reconstruction by Initializing 3D Neural Networks with Physical Inverse Solutions

arXiv: https://arxiv.org/abs/2411.00143 · HTML: https://mlsanity.com/paper/2411.00143/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 83 references that are in the map.
- First posted on arXiv 31 Oct 2024.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Deep learning-based electroencephalography analysis: a systematic review](https://mlsanity.com/paper/1901.05498/) (2019)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [Analyzing Neuroimaging Data Through Recurrent Deep Learning Models](https://mlsanity.com/paper/1810.09945/) (2018)
- [Physics-Informed Bayesian Optimization of Variational Quantum Circuits](https://mlsanity.com/paper/2406.06150/) (2024)
- [MEG Source Localization via Deep Learning](https://mlsanity.com/paper/2012.00588/) (2020)
- [Electromagnetic Source Imaging via a Data-Synthesis-Based Convolutional Encoder-Decoder Network](https://mlsanity.com/paper/2010.12876/) (2020)

## Built on by (most cited first, 1 of 1)

- [Structure-Preserving Correction Learning for Sparse Bayesian Inference in Brain Source Imaging](https://mlsanity.com/paper/2606.07196/) (2026)

## Abstract (arXiv)

Reconstructing brain sources is a fundamental challenge in neuroscience, crucial for understanding brain function and dysfunction. Electroencephalography (EEG) signals have a high temporal resolution. However, identifying the correct spatial location of brain sources from these signals remains difficult due to the ill-posed structure of the problem. Traditional methods predominantly rely on manually crafted priors, missing the flexibility of data-driven learning, while recent deep learning approaches focus on end-to-end learning, typically using the physical information of the forward model only for generating training data. We propose the novel hybrid method 3D-PIUNet for EEG source localization that effectively integrates the strengths of traditional and deep learning techniques. 3D-PIUNet starts from an initial physics-informed estimate by using the pseudo inverse to map from measurements to source space. Secondly, by viewing the brain as a 3D volume, we use a 3D convolutional U-Net to capture spatial dependencies and refine the solution according to the learned data prior. Training the model relies on simulated pseudo-realistic brain source data, covering different source distributions. Trained on this data, our model significantly improves spatial accuracy, demonstrating superior performance over both traditional and end-to-end data-driven methods. Additionally, we validate our findings with real EEG data from a visual task, where 3D-PIUNet successfully identifies the visual cortex and reconstructs the expected temporal behavior, thereby showcasing its practical applicability.