Prediction techniques for dynamic imaging with online primal-dual methods

TL;DR

This paper advances online primal-dual methods for dynamic imaging by providing a more concise analysis, relaxing conditions, and developing improved dual predictors, with demonstrated effectiveness in image stabilization and medical imaging.

Contribution

It offers a simplified analysis of predictive online primal-dual methods and introduces improved dual predictors for dynamic imaging applications.

Findings

Enhanced image stabilization performance

Effective dynamic positron emission tomography results

Relaxed conditions for dual predictor design

Abstract

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.