# Enhancing Electrical Impedance Tomography reconstruction using Learned Half-Quadratic Splitting Networks with Anderson Acceleration

arXiv: https://arxiv.org/abs/2304.14491 · HTML: https://mlsanity.com/paper/2304.14491/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 49 references that are in the map.
- First posted on arXiv 16 Apr 2023.

## Builds on (most cited first, 15 of 15)

- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Globally Convergent Type-I Anderson Acceleration for Non-Smooth Fixed-Point Iterations](https://mlsanity.com/paper/1808.03971/) (2018)
- [Deep D-bar: Real time Electrical Impedance Tomography Imaging with Deep Neural Networks](https://mlsanity.com/paper/1711.03180/) (2017)
- [Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithms](https://mlsanity.com/paper/2103.10182/) (2021)
- [Anderson Acceleration for Reinforcement Learning](https://mlsanity.com/paper/1809.09501/) (2018)
- [Physics Embedded Machine Learning for Electromagnetic Data Imaging](https://mlsanity.com/paper/2207.12607/) (2022)
- [Beltrami-Net: Domain Independent Deep D-bar Learning for Absolute Imaging with Electrical Impedance Tomography (a-EIT)](https://mlsanity.com/paper/1811.12830/) (2018)
- [Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems](https://mlsanity.com/paper/2103.15138/) (2021)
- [Deep Unrolled Recovery in Sparse Biological Imaging](https://mlsanity.com/paper/2109.14025/) (2021)
- [Regularized Anderson Acceleration for Off-Policy Deep Reinforcement Learning](https://mlsanity.com/paper/1909.03245/) (2019)
- [Anderson Acceleration of Proximal Gradient Methods](https://mlsanity.com/paper/1910.08590/) (2019)
- [Learned Half-Quadratic Splitting Network for MR Image Reconstruction](https://mlsanity.com/paper/2112.09760/) (2021)
- [Nonlinear Acceleration of Momentum and Primal-Dual Algorithms](https://mlsanity.com/paper/1810.04539/) (2018)
- [Nesterov's Acceleration For Approximate Newton](https://mlsanity.com/paper/1710.08496/) (2017)
- [Stable Anderson Acceleration for Deep Learning](https://mlsanity.com/paper/2110.14813/) (2021)

## Built on by (most cited first, 2 of 2)

- [Deep Unrolling Networks with Recurrent Momentum Acceleration for Nonlinear Inverse Problems](https://mlsanity.com/paper/2307.16120/) (2023)
- [Multi-Scale Frequency-Enhanced Deep D-bar Method for Electrical Impedance Tomography](https://mlsanity.com/paper/2407.03335/) (2024)

## Abstract (arXiv)

Electrical Impedance Tomography (EIT) is widely applied in medical diagnosis, industrial inspection, and environmental monitoring. Combining the physical principles of the imaging system with the advantages of data-driven deep learning networks, physics-embedded deep unrolling networks have recently emerged as a promising solution in computational imaging. However, the inherent nonlinear and ill-posed properties of EIT image reconstruction still present challenges to existing methods in terms of accuracy and stability. To tackle this challenge, we propose the learned half-quadratic splitting (HQSNet) algorithm for incorporating physics into learning-based EIT imaging. We then apply Anderson acceleration (AA) to the HQSNet algorithm, denoted as AA-HQSNet, which can be interpreted as AA applied to the Gauss-Newton step and the learned proximal gradient descent step of the HQSNet, respectively. AA is a widely-used technique for accelerating the convergence of fixed-point iterative algorithms and has gained significant interest in numerical optimization and machine learning. However, the technique has received little attention in the inverse problems community thus far. Employing AA enhances the convergence rate compared to the standard HQSNet while simultaneously avoiding artifacts in the reconstructions. Lastly, we conduct rigorous numerical and visual experiments to show that the AA module strengthens the HQSNet, leading to robust, accurate, and considerably superior reconstructions compared to state-of-the-art methods. Our Anderson acceleration scheme to enhance HQSNet is generic and can be applied to improve the performance of various physics-embedded deep learning methods.