# A Self-Supervised Approach to Reconstruction in Sparse X-Ray Computed Tomography

arXiv: https://arxiv.org/abs/2211.00002 · HTML: https://mlsanity.com/paper/2211.00002/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 47 references that are in the map.
- First posted on arXiv 30 Oct 2022.

## Builds on (most cited first, 14 of 14)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [Radon Inversion via Deep Learning](https://mlsanity.com/paper/1808.03015/) (2018)
- [Task-Aware Compressed Sensing with Generative Adversarial Networks](https://mlsanity.com/paper/1802.01284/) (2018)
- [Training deep learning based image denoisers from undersampled measurements without ground truth and without image prior](https://mlsanity.com/paper/1806.00961/) (2018)
- [Unsupervised Deep Basis Pursuit: Learning inverse problems without ground-truth data](https://mlsanity.com/paper/1910.13110/) (2019)
- [Training Image Estimators without Image Ground-Truth](https://mlsanity.com/paper/1906.05775/) (2019)
- [Fast Compressive Sensing Recovery Using Generative Models with Structured Latent Variables](https://mlsanity.com/paper/1902.06913/) (2019)
- [A hierarchical approach to deep learning and its application to tomographic reconstruction](https://mlsanity.com/paper/1912.07743/) (2019)
- [Image Reconstruction for MRI using Deep CNN Priors Trained without Groundtruth](https://mlsanity.com/paper/2204.04771/) (2022)
- [Deep Learning Based Computed Tomography Whys and Wherefores](https://mlsanity.com/paper/1904.03908/) (2019)
- [Sparse Matrix-Based HPC Tomography](https://mlsanity.com/paper/2003.12677/) (2020)

## Built on by (most cited first, 2 of 2)

- [Discovering Structure From Corruption for Unsupervised Image Reconstruction](https://mlsanity.com/paper/2304.05589/) (2023)
- [Riemannian AmbientFlow: Towards Simultaneous Manifold Learning and Generative Modeling from Corrupted Data](https://mlsanity.com/paper/2601.18728/) (2026)

## Abstract (arXiv)

Computed tomography has propelled scientific advances in fields from biology to materials science. This technology allows for the elucidation of 3-dimensional internal structure by the attenuation of x-rays through an object at different rotations relative to the beam. By imaging 2-dimensional projections, a 3-dimensional object can be reconstructed through a computational algorithm. Imaging at a greater number of rotation angles allows for improved reconstruction. However, taking more measurements increases the x-ray dose and may cause sample damage. Deep neural networks have been used to transform sparse 2-D projection measurements to a 3-D reconstruction by training on a dataset of known similar objects. However, obtaining high-quality object reconstructions for the training dataset requires high x-ray dose measurements that can destroy or alter the specimen before imaging is complete. This becomes a chicken-and-egg problem: high-quality reconstructions cannot be generated without deep learning, and the deep neural network cannot be learned without the reconstructions. This work develops and validates a self-supervised probabilistic deep learning technique, the physics-informed variational autoencoder, to solve this problem. A dataset consisting solely of sparse projection measurements from each object is used to jointly reconstruct all objects of the set. This approach has the potential to allow visualization of fragile samples with x-ray computed tomography. We release our code for reproducing our results at: https://github.com/vganapati/CT_PVAE .