# Near-Exact Recovery for Tomographic Inverse Problems via Deep Learning

arXiv: https://arxiv.org/abs/2206.07050 · HTML: https://mlsanity.com/paper/2206.07050/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 14 Jun 2022.

## Builds on (most cited first, 30 of 31)

- [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)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Low-Dose CT with a Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)](https://mlsanity.com/paper/1702.00288/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [The One Hundred Layers Tiramisu: Fully Convolutional DenseNets for Semantic Segmentation](https://mlsanity.com/paper/1611.09326/) (2016)
- [A deep convolutional neural network using directional wavelets for low-dose X-ray CT reconstruction](https://mlsanity.com/paper/1610.09736/) (2016)
- [Advancing machine learning for MR image reconstruction with an open competition: Overview of the 2019 fastMRI challenge](https://mlsanity.com/paper/2001.02518/) (2020)
- [Solving Inverse Problems With Deep Neural Networks -- Robustness Included?](https://mlsanity.com/paper/2011.04268/) (2020)
- [Measuring Robustness in Deep Learning Based Compressive Sensing](https://mlsanity.com/paper/2102.06103/) (2021)
- [Momentum-Net: Fast and convergent iterative neural network for inverse problems](https://mlsanity.com/paper/1907.11818/) (2019)
- [Recurrent Inference Machines for Solving Inverse Problems](https://mlsanity.com/paper/1706.04008/) (2017)
- [Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for Limited Angle Computed Tomography](https://mlsanity.com/paper/1811.04602/) (2018)
- [Model Adaptation for Inverse Problems in Imaging](https://mlsanity.com/paper/2012.00139/) (2020)
- [Feasibility-based Fixed Point Networks](https://mlsanity.com/paper/2104.14090/) (2021)
- [Results of the 2020 fastMRI Challenge for Machine Learning MR Image Reconstruction](https://mlsanity.com/paper/2012.06318/) (2020)
- [Do CNNs solve the CT inverse problem?](https://mlsanity.com/paper/2005.10755/) (2020)
- [Low-Dose CT with Deep Learning Regularization via Proximal Forward Backward Splitting](https://mlsanity.com/paper/1909.09773/) (2019)
- [On the Convergence Rate of Projected Gradient Descent for a Back-Projection based Objective](https://mlsanity.com/paper/2005.00959/) (2020)
- [dAUTOMAP: decomposing AUTOMAP to achieve scalability and enhance performance](https://mlsanity.com/paper/1909.10995/) (2019)

## Built on by (most cited first, 13 of 13)

- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance](https://mlsanity.com/paper/2312.16519/) (2023)
- [Multilevel CNNs for Parametric PDEs](https://mlsanity.com/paper/2304.00388/) (2023)
- [Gradient-Based Geometry Learning for Fan-Beam CT Reconstruction](https://mlsanity.com/paper/2212.02177/) (2022)
- [Slicer Networks](https://mlsanity.com/paper/2401.09833/) (2024)
- [Limited-Angle Tomography Reconstruction via Deep End-To-End Learning on Synthetic Data](https://mlsanity.com/paper/2309.06948/) (2023)
- [Improving Automated Hemorrhage Detection in Sparse-view Computed Tomography via Deep Convolutional Neural Network based Artifact Reduction](https://mlsanity.com/paper/2303.09340/) (2023)
- [Non-Asymptotic Uncertainty Quantification in High-Dimensional Learning](https://mlsanity.com/paper/2407.13666/) (2024)
- [Enhanced Low-Dose CT Image Reconstruction by Domain and Task Shifting Gaussian Denoisers](https://mlsanity.com/paper/2403.03551/) (2024)
- [Self-Supervised Denoiser Framework](https://mlsanity.com/paper/2411.19593/) (2024)
- [Let's Enhance: A Deep Learning Approach to Extreme Deblurring of Text Images](https://mlsanity.com/paper/2211.10103/) (2022)
- [Improving the Generalisation of Learned Reconstruction Frameworks](https://mlsanity.com/paper/2511.12730/) (2025)
- [Diffusion Based Unpaired Data Learning for Inverse Problems](https://mlsanity.com/paper/2609.01370/) (2026)

## Abstract (arXiv)

This work is concerned with the following fundamental question in scientific machine learning: Can deep-learning-based methods solve noise-free inverse problems to near-perfect accuracy? Positive evidence is provided for the first time, focusing on a prototypical computed tomography (CT) setup. We demonstrate that an iterative end-to-end network scheme enables reconstructions close to numerical precision, comparable to classical compressed sensing strategies. Our results build on our winning submission to the recent AAPM DL-Sparse-View CT Challenge. Its goal was to identify the state-of-the-art in solving the sparse-view CT inverse problem with data-driven techniques. A specific difficulty of the challenge setup was that the precise forward model remained unknown to the participants. Therefore, a key feature of our approach was to initially estimate the unknown fanbeam geometry in a data-driven calibration step. Apart from an in-depth analysis of our methodology, we also demonstrate its state-of-the-art performance on the open-access real-world dataset LoDoPaB CT.