# An Adversarial Learning Based Approach for Unknown View Tomographic Reconstruction

arXiv: https://arxiv.org/abs/2108.09873 · HTML: https://mlsanity.com/paper/2108.09873/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 65 references that are in the map.
- First posted on arXiv 23 Aug 2021.

## Builds on (most cited first, 23 of 23)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [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)
- [Low-Dose CT with a Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)](https://mlsanity.com/paper/1702.00288/) (2017)
- [Low Dose CT Image Denoising Using a Generative Adversarial Network with Wasserstein Distance and Perceptual Loss](https://mlsanity.com/paper/1708.00961/) (2017)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [Compressed Sensing MRI Reconstruction using a Generative Adversarial Network with a Cyclic Loss](https://mlsanity.com/paper/1709.00753/) (2017)
- [Computed Tomography Reconstruction Using Deep Image Prior and Learned Reconstruction Methods](https://mlsanity.com/paper/2003.04989/) (2020)
- [Can Deep Learning Outperform Modern Commercial CT Image Reconstruction Methods?](https://mlsanity.com/paper/1811.03691/) (2018)
- [Fast Steerable Principal Component Analysis](https://mlsanity.com/paper/1412.0781/) (2014)
- [3D ab initio modeling in cryo-EM by autocorrelation analysis](https://mlsanity.com/paper/1710.08076/) (2017)
- [Geometric Invariants for Sparse Unknown View Tomography](https://mlsanity.com/paper/1811.09940/) (2018)
- [3D unknown view tomography via rotation invariants](https://mlsanity.com/paper/2003.10107/) (2020)
- [A Fourier-based Approach for Iterative 3D Reconstruction from Cryo-EM Images](https://mlsanity.com/paper/1307.5824/) (2013)
- [Two-Dimensional Tomography From Noisy Projection Tilt Series Taken At Unknown View Angles With Non-Uniform Distribution](https://mlsanity.com/paper/1905.10343/) (2019)
- [UVTomo-GAN: An adversarial learning based approach for unknown view X-ray tomographic reconstruction](https://mlsanity.com/paper/2102.04590/) (2021)
- [MSR-GAN: Multi-Segment Reconstruction via Adversarial Learning](https://mlsanity.com/paper/2102.09494/) (2021)

## Abstract (arXiv)

The goal of 2D tomographic reconstruction is to recover an image given its projections from various views. It is often presumed that projection angles associated with the projections are known in advance. Under certain situations, however, these angles are known only approximately or are completely unknown. It becomes more challenging to reconstruct the image from a collection of random projections. We propose an adversarial learning based approach to recover the image and the projection angle distribution by matching the empirical distribution of the measurements with the generated data. Fitting the distributions is achieved through solving a min-max game between a generator and a critic based on Wasserstein generative adversarial network structure. To accommodate the update of the projection angle distribution through gradient back propagation, we approximate the loss using the Gumbel-Softmax reparameterization of samples from discrete distributions. Our theoretical analysis verifies the unique recovery of the image and the projection distribution up to a rotation and reflection upon convergence. Our extensive numerical experiments showcase the potential of our method to accurately recover the image and the projection angle distribution under noise contamination.