# Prediction techniques for dynamic imaging with online primal-dual methods

arXiv: https://arxiv.org/abs/2405.02497 · HTML: https://mlsanity.com/paper/2405.02497/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 3 May 2024.

## Builds on (most cited first, 20 of 20)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Dynamical Models and Tracking Regret in Online Convex Programming](https://mlsanity.com/paper/1301.1254/) (2013)
- [Time-Varying Convex Optimization: Time-Structured Algorithms and Applications](https://mlsanity.com/paper/2006.08500/) (2020)
- [A Class of Prediction-Correction Methods for Time-Varying Convex Optimization](https://mlsanity.com/paper/1509.05196/) (2015)
- [Online Proximal-ADMM For Time-varying Constrained Convex Optimization](https://mlsanity.com/paper/2005.03267/) (2020)
- [Prediction-Correction Algorithms for Time-Varying Constrained Optimization](https://mlsanity.com/paper/1611.03681/) (2016)
- [Online Primal-Dual Methods with Measurement Feedback for Time-Varying Convex Optimization](https://mlsanity.com/paper/1804.05159/) (2018)
- [Regrets of Proximal Method of Multipliers for Online Non-convex Optimization with Long Term Constraints](https://mlsanity.com/paper/2204.10986/) (2022)
- [A Variational Reconstruction Method for Undersampled Dynamic X-ray Tomography based on Physical Motion Models](https://mlsanity.com/paper/1705.06079/) (2017)
- [Online convex optimization and no-regret learning: Algorithms, guarantees and applications](https://mlsanity.com/paper/1804.04529/) (2018)
- [Dual Prediction-Correction Methods for Linearly Constrained Time-Varying Convex Programs](https://mlsanity.com/paper/1709.05850/) (2017)
- [Running Primal-Dual Gradient Method for Time-Varying Nonconvex Problems](https://mlsanity.com/paper/1812.00613/) (2018)
- [Distributed Online Convex Optimization with Improved Dynamic Regret](https://mlsanity.com/paper/1911.05127/) (2019)
- [Online Gradient Descent for Linear Dynamical Systems](https://mlsanity.com/paper/1912.09311/) (2019)
- [Introduction to Nonsmooth Analysis and Optimization](https://mlsanity.com/paper/2001.00216/) (2020)
- [Testing and non-linear preconditioning of the proximal point method](https://mlsanity.com/paper/1703.05705/) (2017)
- [First-order primal-dual methods for nonsmooth nonconvex optimisation](https://mlsanity.com/paper/1910.00115/) (2019)
- [Predictive online optimisation with applications to optical flow](https://mlsanity.com/paper/2002.03053/) (2020)
- [A nonsmooth primal-dual method with interwoven PDE constraint solver](https://mlsanity.com/paper/2211.04807/) (2022)

## Built on by (most cited first, 1 of 1)

- [Online optimisation for dynamic electrical impedance tomography](https://mlsanity.com/paper/2412.12944/) (2024)

## Abstract (arXiv)

Online optimisation facilitates the solution of dynamic inverse problems, such as image stabilisation, fluid flow monitoring, and dynamic medical imaging. In this paper, we improve upon previous work on predictive online primal-dual methods on two fronts. Firstly, we provide a more concise analysis that symmetrises previously unsymmetric regret bounds, and relaxes previous restrictive conditions on the dual predictor. Secondly, based on the latter, we develop several improved dual predictors. We numerically demonstrate their efficacy in image stabilisation and dynamic positron emission tomography.