# Gravitationally Lensed Black Hole Emission Tomography

arXiv: https://arxiv.org/abs/2204.03715 · HTML: https://mlsanity.com/paper/2204.03715/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 50 references that are in the map.
- First posted on arXiv 7 Apr 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [Dynamic Neural Radiance Fields for Monocular 4D Facial Avatar Reconstruction](https://mlsanity.com/paper/2012.03065/) (2020)
- [Animatable Neural Radiance Fields for Modeling Dynamic Human Bodies](https://mlsanity.com/paper/2105.02872/) (2021)
- [Computational Imaging for VLBI Image Reconstruction](https://mlsanity.com/paper/1512.01413/) (2015)
- [Multi-view polarimetric scattering cloud tomography and retrieval of droplet size](https://mlsanity.com/paper/2005.11423/) (2020)

## Built on by (most cited first, 22 of 22)

- [NeRFPlayer: A Streamable Dynamic Scene Representation with Decomposed Neural Radiance Fields](https://mlsanity.com/paper/2210.15947/) (2022)
- [SparseGS: Sparse View Synthesis using 3D Gaussian Splatting](https://mlsanity.com/paper/2312.00206/) (2023)
- [Advances in 3D Generation: A Survey](https://mlsanity.com/paper/2401.17807/) (2024)
- [SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems](https://mlsanity.com/paper/2410.04479/) (2024)
- [Exact-NeRF: An Exploration of a Precise Volumetric Parameterization for Neural Radiance Fields](https://mlsanity.com/paper/2211.12285/) (2022)
- [Reconstructing 4D Spatial Intelligence: A Survey](https://mlsanity.com/paper/2507.21045/) (2025)
- [Single View Refractive Index Tomography with Neural Fields](https://mlsanity.com/paper/2309.04437/) (2023)
- [NeRFs: The Search for the Best 3D Representation](https://mlsanity.com/paper/2308.02751/) (2023)
- [Radar Fields: An Extension of Radiance Fields to SAR](https://mlsanity.com/paper/2312.12961/) (2023)
- [Strong Lensing Source Reconstruction Using Continuous Neural Fields](https://mlsanity.com/paper/2206.14820/) (2022)
- [Orbital Polarimetric Tomography of a Flare Near the Sagittarius A* Supermassive Black Hole](https://mlsanity.com/paper/2310.07687/) (2023)
- [Revealing the 3D Cosmic Web through Gravitationally Constrained Neural Fields](https://mlsanity.com/paper/2504.15262/) (2025)
- [UGoDIT: Unsupervised Group Deep Image Prior Via Transferable Weights](https://mlsanity.com/paper/2505.11720/) (2025)
- [Recovering a Molecule's 3D Dynamics from Liquid-phase Electron Microscopy Movies](https://mlsanity.com/paper/2308.11927/) (2023)
- [Dynamic Black-hole Emission Tomography with Physics-informed Neural Fields](https://mlsanity.com/paper/2602.08029/) (2026)
- [Success Probability in Multi-View Imaging](https://mlsanity.com/paper/2407.21027/) (2024)
- [Spectra-to-Structure and Structure-to-Spectra Inference Across the Periodic Table](https://mlsanity.com/paper/2506.11908/) (2025)
- [Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity](https://mlsanity.com/paper/2507.15775/) (2025)
- [Revealing Fine Structure in Protoplanetary Disks with Physics Constrained Neural Fields](https://mlsanity.com/paper/2509.03623/) (2025)
- [NERD: Network-Regularized Diffusion Sampling For 3D Computed Tomography](https://mlsanity.com/paper/2511.14680/) (2025)
- [A Principled Self-Referenced Early Stopping Approach for Deep Image Prior](https://mlsanity.com/paper/2605.25299/) (2026)
- [Image Fidelity is Not Field Fidelity: Joint Thermodynamic Reconstruction and Error Localization in Neural Tomography](https://mlsanity.com/paper/2609.28868/) (2026)

## Abstract (arXiv)

Measurements from the Event Horizon Telescope enabled the visualization of light emission around a black hole for the first time. So far, these measurements have been used to recover a 2D image under the assumption that the emission field is static over the period of acquisition. In this work, we propose BH-NeRF, a novel tomography approach that leverages gravitational lensing to recover the continuous 3D emission field near a black hole. Compared to other 3D reconstruction or tomography settings, this task poses two significant challenges: first, rays near black holes follow curved paths dictated by general relativity, and second, we only observe measurements from a single viewpoint. Our method captures the unknown emission field using a continuous volumetric function parameterized by a coordinate-based neural network, and uses knowledge of Keplerian orbital dynamics to establish correspondence between 3D points over time. Together, these enable BH-NeRF to recover accurate 3D emission fields, even in challenging situations with sparse measurements and uncertain orbital dynamics. This work takes the first steps in showing how future measurements from the Event Horizon Telescope could be used to recover evolving 3D emission around the supermassive black hole in our Galactic center.