# Convergent Data-driven Regularizations for CT Reconstruction

arXiv: https://arxiv.org/abs/2212.07786 · HTML: https://mlsanity.com/paper/2212.07786/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 47 references that are in the map.
- First posted on arXiv 14 Dec 2022.

## Builds on (most cited first, 22 of 22)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (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)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models](https://mlsanity.com/paper/1703.09912/) (2017)
- [Computed Tomography Reconstruction Using Deep Image Prior and Learned Reconstruction Methods](https://mlsanity.com/paper/2003.04989/) (2020)
- [Total Deep Variation for Linear Inverse Problems](https://mlsanity.com/paper/2001.05005/) (2020)
- [Radon Inversion via Deep Learning](https://mlsanity.com/paper/1808.03015/) (2018)
- [Learning the optimal Tikhonov regularizer for inverse problems](https://mlsanity.com/paper/2106.06513/) (2021)
- [Insights into analysis operator learning: From patch-based sparse models to higher-order MRFs](https://mlsanity.com/paper/1401.2804/) (2014)
- [Fast and Provable ADMM for Learning with Generative Priors](https://mlsanity.com/paper/1907.03343/) (2019)
- [Controlling Neural Networks via Energy Dissipation](https://mlsanity.com/paper/1904.03081/) (2019)
- [Regularization of Inverse Problems: Deep Equilibrium Models versus Bilevel Learning](https://mlsanity.com/paper/2206.13193/) (2022)

## Built on by (most cited first, 5 of 5)

- [A Lifted Bregman Formulation for the Inversion of Deep Neural Networks](https://mlsanity.com/paper/2303.01965/) (2023)
- [Learned Regularization for Inverse Problems: Insights from a Spectral Model](https://mlsanity.com/paper/2312.09845/) (2023)
- [Learned reconstruction methods for inverse problems: sample error estimates](https://mlsanity.com/paper/2312.14078/) (2023)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)
- [Virtual-mask Informed Prior for Sparse-view Dual-Energy CT Reconstruction](https://mlsanity.com/paper/2504.07753/) (2025)

## Abstract (arXiv)

The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend on the measured data continuously, regularization is needed to re-establish a continuous dependence. In this work, we investigate simple, but yet still provably convergent approaches to learning linear regularization methods from data. More specifically, we analyze two approaches: One generic linear regularization that learns how to manipulate the singular values of the linear operator in an extension of our previous work, and one tailored approach in the Fourier domain that is specific to CT-reconstruction. We prove that such approaches become convergent regularization methods as well as the fact that the reconstructions they provide are typically much smoother than the training data they were trained on. Finally, we compare the spectral as well as the Fourier-based approaches for CT-reconstruction numerically, discuss their advantages and disadvantages and investigate the effect of discretization errors at different resolutions.