# Model-corrected learned primal-dual models for fast limited-view photoacoustic tomography

arXiv: https://arxiv.org/abs/2304.01963 · HTML: https://mlsanity.com/paper/2304.01963/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 57 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 27 of 27)

- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction](https://mlsanity.com/paper/2211.12340/) (2022)
- [Learning Maximally Monotone Operators for Image Recovery](https://mlsanity.com/paper/2012.13247/) (2020)
- [Learned convex regularizers for inverse problems](https://mlsanity.com/paper/2008.02839/) (2020)
- [Learned reconstruction methods with convergence guarantees](https://mlsanity.com/paper/2206.05431/) (2022)
- [Model based learning for accelerated, limited-view 3D photoacoustic tomography](https://mlsanity.com/paper/1708.09832/) (2017)
- [Deep Learning in Photoacoustic Tomography: Current approaches and future directions](https://mlsanity.com/paper/2009.07608/) (2020)
- [Deep learning for biomedical photoacoustic imaging: A review](https://mlsanity.com/paper/2011.02744/) (2020)
- [Multi-Scale Learned Iterative Reconstruction](https://mlsanity.com/paper/1908.00936/) (2019)
- [i-RIM applied to the fastMRI challenge](https://mlsanity.com/paper/1910.08952/) (2019)
- [A Partially Learned Algorithm for Joint Photoacoustic Reconstruction and Segmentation](https://mlsanity.com/paper/1906.07499/) (2019)
- [Approximate k-space models and Deep Learning for fast photoacoustic reconstruction](https://mlsanity.com/paper/1807.03191/) (2018)
- [Variational regularisation for inverse problems with imperfect forward operators and general noise models](https://mlsanity.com/paper/2005.14131/) (2020)
- [Deep network series for large-scale high-dynamic range imaging](https://mlsanity.com/paper/2210.16060/) (2022)
- [Memory Efficient Invertible Neural Networks for 3D Photoacoustic Imaging](https://mlsanity.com/paper/2204.11850/) (2022)
- [Chambolle-Pock's Primal-Dual Method with Mismatched Adjoint](https://mlsanity.com/paper/2201.04928/) (2022)

## Built on by (most cited first, 6 of 6)

- [Glimpse: Generalized Locality for Scalable and Robust CT](https://mlsanity.com/paper/2401.00816/) (2024)
- [Inverse Problems with Learned Forward Operators](https://mlsanity.com/paper/2311.12528/) (2023)
- [Domain independent post-processing with graph U-nets: Applications to Electrical Impedance Tomographic Imaging](https://mlsanity.com/paper/2305.05020/) (2023)
- [Limited-View Photoacoustic Imaging Reconstruction Via High-quality Self-supervised Neural Representation](https://mlsanity.com/paper/2407.03663/) (2024)
- [Fast algorithms enabling optimization and deep learning for photoacoustic tomography in a circular detection geometry](https://mlsanity.com/paper/2510.24687/) (2025)
- [Matrix-Free Photoacoustic Image Reconstruction via Sensor-Token Self-Attention](https://mlsanity.com/paper/2607.25576/) (2026)

## Abstract (arXiv)

Learned iterative reconstructions hold great promise to accelerate tomographic imaging with empirical robustness to model perturbations. Nevertheless, an adoption for photoacoustic tomography is hindered by the need to repeatedly evaluate the computational expensive forward model. Computational feasibility can be obtained by the use of fast approximate models, but a need to compensate model errors arises. In this work we advance the methodological and theoretical basis for model corrections in learned image reconstructions by embedding the model correction in a learned primal-dual framework. Here, the model correction is jointly learned in data space coupled with a learned updating operator in image space within an unrolled end-to-end learned iterative reconstruction approach. The proposed formulation allows an extension to a primal-dual deep equilibrium model providing fixed-point convergence as well as reduced memory requirements for training. We provide theoretical and empirical insights into the proposed models with numerical validation in a realistic 2D limited-view setting. The model-corrected learned primal-dual methods show excellent reconstruction quality with fast inference times and thus providing a methodological basis for real-time capable and scalable iterative reconstructions in photoacoustic tomography.