# Stochastic Primal-Dual Deep Unrolling

arXiv: https://arxiv.org/abs/2110.10093 · HTML: https://mlsanity.com/paper/2110.10093/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 56 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [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)
- [SGD: General Analysis and Improved Rates](https://mlsanity.com/paper/1901.09401/) (2019)
- [Katyusha: The First Direct Acceleration of Stochastic Gradient Methods](https://mlsanity.com/paper/1603.05953/) (2016)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [A Proximal Stochastic Gradient Method with Progressive Variance Reduction](https://mlsanity.com/paper/1403.4699/) (2014)
- [An Online Plug-and-Play Algorithm for Regularized Image Reconstruction](https://mlsanity.com/paper/1809.04693/) (2018)
- [One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models](https://mlsanity.com/paper/1703.09912/) (2017)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [Learned convex regularizers for inverse problems](https://mlsanity.com/paper/2008.02839/) (2020)
- [Tight Complexity Bounds for Optimizing Composite Objectives](https://mlsanity.com/paper/1605.08003/) (2016)
- [An optimal randomized incremental gradient method](https://mlsanity.com/paper/1507.02000/) (2015)
- [End-to-end reconstruction meets data-driven regularization for inverse problems](https://mlsanity.com/paper/2106.03538/) (2021)
- [Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications](https://mlsanity.com/paper/1706.04957/) (2017)
- [Equivariant neural networks for inverse problems](https://mlsanity.com/paper/2102.11504/) (2021)
- [Task adapted reconstruction for inverse problems](https://mlsanity.com/paper/1809.00948/) (2018)
- [A Fast Stochastic Plug-and-Play ADMM for Imaging Inverse Problems](https://mlsanity.com/paper/2006.11630/) (2020)
- [The Practicality of Stochastic Optimization in Imaging Inverse Problems](https://mlsanity.com/paper/1910.10100/) (2019)
- [Sharp Time--Data Tradeoffs for Linear Inverse Problems](https://mlsanity.com/paper/1507.04793/) (2015)
- [Rest-Katyusha: Exploiting the Solution's Structure via Scheduled Restart Schemes](https://mlsanity.com/paper/1803.02246/) (2018)

## Built on by (most cited first, 4 of 4)

- [Learned reconstruction methods with convergence guarantees](https://mlsanity.com/paper/2206.05431/) (2022)
- [Equivariance Regularization for Image Reconstruction](https://mlsanity.com/paper/2202.05062/) (2022)
- [Operator Sketching for Deep Unrolling Networks](https://mlsanity.com/paper/2203.11156/) (2022)
- [Sparse View Tomographic Reconstruction of Elongated Objects using Learned Primal-Dual Networks](https://mlsanity.com/paper/2403.02820/) (2024)

## Abstract (arXiv)

We propose a new type of efficient deep-unrolling networks for solving imaging inverse problems. Conventional deep-unrolling methods require full forward operator and its adjoint across each layer, and hence can be significantly more expensive computationally as compared with other end-to-end methods that are based on post-processing of model-based reconstructions, especially for 3D image reconstruction tasks. We develop a stochastic (ordered-subsets) variant of the classical learned primal-dual (LPD), which is a state-of-the-art unrolling network for tomographic image reconstruction. The proposed learned stochastic primal-dual (LSPD) network only uses subsets of the forward and adjoint operators and offers considerable computational efficiency. We provide theoretical analysis of a special case of our LSPD framework, suggesting that it has the potential to achieve image reconstruction quality competitive with the full-batch LPD while requiring only a fraction of the computation. The numerical results for two different X-ray computed tomography (CT) imaging tasks (namely, low-dose and sparse-view CT) corroborate this theoretical finding, demonstrating the promise of LSPD networks for large-scale imaging problems.