# Learning end-to-end inversion of circular Radon transforms in the partial radial setup

arXiv: https://arxiv.org/abs/2308.14144 · HTML: https://mlsanity.com/paper/2308.14144/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 27 Aug 2023.

## Builds on (most cited first, 17 of 17)

- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [A deep convolutional neural network using directional wavelets for low-dose X-ray CT reconstruction](https://mlsanity.com/paper/1610.09736/) (2016)
- [Deep Bayesian Inversion](https://mlsanity.com/paper/1811.05910/) (2018)
- [Fully Dense UNet for 2D Sparse Photoacoustic Tomography Artifact Removal](https://mlsanity.com/paper/1808.10848/) (2018)
- [Model based learning for accelerated, limited-view 3D photoacoustic tomography](https://mlsanity.com/paper/1708.09832/) (2017)
- [End-to-end reconstruction meets data-driven regularization for inverse problems](https://mlsanity.com/paper/2106.03538/) (2021)
- [Equivariant neural networks for inverse problems](https://mlsanity.com/paper/2102.11504/) (2021)
- [Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priors](https://mlsanity.com/paper/2107.02926/) (2021)
- [Deep Learning in Photoacoustic Tomography: Current approaches and future directions](https://mlsanity.com/paper/2009.07608/) (2020)
- [Learning Regularization Parameters of Inverse Problems via Deep Neural Networks](https://mlsanity.com/paper/2104.06594/) (2021)
- [Deep Learning for Photoacoustic Tomography from Sparse Data](https://mlsanity.com/paper/1704.04587/) (2017)
- [The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problems](https://mlsanity.com/paper/2202.07773/) (2022)
- [A Partially Learned Algorithm for Joint Photoacoustic Reconstruction and Segmentation](https://mlsanity.com/paper/1906.07499/) (2019)

## Abstract (arXiv)

We present a deep learning-based computational algorithm for inversion of circular Radon transforms in the partial radial setup, arising in photoacoustic tomography. We first demonstrate that the truncated singular value decomposition-based method, which is the only traditional algorithm available to solve this problem, leads to severe artifacts which renders the reconstructed field as unusable. With the objective of overcoming this computational bottleneck, we train a ResBlock based U-Net to recover the inferred field that directly operates on the measured data. Numerical results with augmented Shepp-Logan phantoms, in the presence of noisy full and limited view data, demonstrate the superiority of the proposed algorithm.