# A Geometry-Informed Deep Learning Framework for Ultra-Sparse 3D Tomographic Image Reconstruction

arXiv: https://arxiv.org/abs/2105.11692 · HTML: https://mlsanity.com/paper/2105.11692/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 81 references that are in the map.
- First posted on arXiv 25 May 2021.

## Builds on (most cited first, 30 of 36)

- [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)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Multimodal Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1804.04732/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [SynSin: End-to-end View Synthesis from a Single Image](https://mlsanity.com/paper/1912.08804/) (2019)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [Learning a Multi-View Stereo Machine](https://mlsanity.com/paper/1708.05375/) (2017)
- [Unsupervised Learning of Probably Symmetric Deformable 3D Objects from Images in the Wild](https://mlsanity.com/paper/1911.11130/) (2019)
- [Neural Volumes: Learning Dynamic Renderable Volumes from Images](https://mlsanity.com/paper/1906.07751/) (2019)
- [Escaping Plato's Cave: 3D Shape From Adversarial Rendering](https://mlsanity.com/paper/1811.11606/) (2018)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Perspective Transformer Nets: Learning Single-View 3D Object Reconstruction without 3D Supervision](https://mlsanity.com/paper/1612.00814/) (2016)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [X2CT-GAN: Reconstructing CT from Biplanar X-Rays with Generative Adversarial Networks](https://mlsanity.com/paper/1905.06902/) (2019)
- [DuDoNet: Dual Domain Network for CT Metal Artifact Reduction](https://mlsanity.com/paper/1907.00273/) (2019)
- [Learning to Reconstruct Shapes from Unseen Classes](https://mlsanity.com/paper/1812.11166/) (2018)
- [Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning](https://mlsanity.com/paper/1904.02816/) (2019)
- [Deep-neural-network based sinogram synthesis for sparse-view CT image reconstruction](https://mlsanity.com/paper/1803.00694/) (2018)
- [Deep Sinogram Completion with Image Prior for Metal Artifact Reduction in CT Images](https://mlsanity.com/paper/2009.07469/) (2020)
- [Learning Spatial Common Sense with Geometry-Aware Recurrent Networks](https://mlsanity.com/paper/1901.00003/) (2018)

## Built on by (most cited first, 11 of 11)

- [DIFR3CT: Latent Diffusion for Probabilistic 3D CT Reconstruction from Few Planar X-Rays](https://mlsanity.com/paper/2408.15118/) (2024)
- [X-ray Dissectography Improves Lung Nodule Detection](https://mlsanity.com/paper/2203.13118/) (2022)
- [SdCT-GAN: Reconstructing CT from Biplanar X-Rays with Self-driven Generative Adversarial Networks](https://mlsanity.com/paper/2309.04960/) (2023)
- [Low-resolution Prior Equilibrium Network for CT Reconstruction](https://mlsanity.com/paper/2401.15663/) (2024)
- [Surf2CT: Cascaded 3D Flow Matching Models for Torso 3D CT Synthesis from Skin Surface](https://mlsanity.com/paper/2505.22511/) (2025)
- [X-ray Dissectography Enables Stereotography to Improve Diagnostic Performance](https://mlsanity.com/paper/2111.15040/) (2021)
- [Enhanced artificial intelligence-based diagnosis using CBCT with internal denoising: Clinical validation for discrimination of fungal ball, sinusitis, and normal cases in the maxillary sinus](https://mlsanity.com/paper/2211.15950/) (2022)
- [GuidedRec: Guiding Ill-Posed Unsupervised Volumetric Recovery](https://mlsanity.com/paper/2405.11977/) (2024)
- [Multi-sensor Learning Enables Information Transfer across Different Sensory Data and Augments Multi-modality Imaging](https://mlsanity.com/paper/2409.19420/) (2024)
- [Novel-view X-ray Projection Synthesis through Geometry-Integrated Deep Learning](https://mlsanity.com/paper/2504.11953/) (2025)
- [Deep learning Based Correction Algorithms for 3D Medical Reconstruction in Computed Tomography and Macroscopic Imaging](https://mlsanity.com/paper/2602.00220/) (2026)

## Abstract (arXiv)

Deep learning affords enormous opportunities to augment the armamentarium of biomedical imaging, albeit its design and implementation have potential flaws. Fundamentally, most deep learning models are driven entirely by data without consideration of any prior knowledge, which dramatically increases the complexity of neural networks and limits the application scope and model generalizability. Here we establish a geometry-informed deep learning framework for ultra-sparse 3D tomographic image reconstruction. We introduce a novel mechanism for integrating geometric priors of the imaging system. We demonstrate that the seamless inclusion of known priors is essential to enhance the performance of 3D volumetric computed tomography imaging with ultra-sparse sampling. The study opens new avenues for data-driven biomedical imaging and promises to provide substantially improved imaging tools for various clinical imaging and image-guided interventions.