# Learning Geometry-Dependent and Physics-Based Inverse Image Reconstruction

arXiv: https://arxiv.org/abs/2007.09522 · HTML: https://mlsanity.com/paper/2007.09522/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [Few-shot Generation of Personalized Neural Surrogates for Cardiac Simulation via Bayesian Meta-Learning](https://mlsanity.com/paper/2210.02967/) (2022)
- [HyPer-EP: Meta-Learning Hybrid Personalized Models for Cardiac Electrophysiology](https://mlsanity.com/paper/2403.15433/) (2024)
- [Neural State-Space Modeling with Latent Causal-Effect Disentanglement](https://mlsanity.com/paper/2209.12387/) (2022)
- [CoMetaPNS: Continually Meta-learning Personalized Neural Surrogates for Cardiac Electrophysiology Simulations](https://mlsanity.com/paper/2606.07488/) (2026)

## Abstract (arXiv)

Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper, we present a new approach to learn inverse imaging that exploit the underlying geometry and physics. We first introduce a non-Euclidean encoding-decoding network that allows us to describe the unknown and measurement variables over their respective geometrical domains. We then learn the geometry-dependent physics in between the two domains by explicitly modeling it via a bipartite graph over the graphical embedding of the two geometry. We applied the presented network to reconstructing electrical activity on the heart surface from body-surface potential. In a series of generalization tasks with increasing difficulty, we demonstrated the improved ability of the presented network to generalize across geometrical changes underlying the data in comparison to its Euclidean alternatives.