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Online optimisation for dynamic electrical impedance tomography

arXiv 2412.12944 ↗First posted 17 Dec 2024math.OC cs.CVcited by 0

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Abstract (arXiv)

Online optimisation studies the convergence of optimisation methods as the data embedded in the problem changes. Based on this idea, we propose a primal dual online method for nonlinear time-discrete inverse problems. We analyse the method through regret theory and demonstrate its performance in real-time monitoring of moving bodies in a fluid with Electrical Impedance Tomography (EIT). To do so, we also prove the second-order differentiability of the Complete Electrode Model (CEM) solution operator on L^∞.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 22 of its 59 references that are in the map. First posted on arXiv 17 Dec 2024.

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References · 22

  1. 2019Introduction to Online Convex Optimizationcited by 793
  2. 2019Online Learning: A Modern Introduction Using Convex Optimizationcited by 407
  3. 2013Dynamical Models and Tracking Regret in Online Convex Programmingcited by 42
  4. 2020Time-Varying Convex Optimization: Time-Structured Algorithms and Applicationscited by 31
  5. 2020Online Proximal-ADMM For Time-varying Constrained Convex Optimizationcited by 10
  6. 2018Online Primal-Dual Methods with Measurement Feedback for Time-Varying Convex Optimizationcited by 6
  7. 2019Ensemble Kalman Methods With Constraintscited by 6
  8. 2022Regrets of Proximal Method of Multipliers for Online Non-convex Optimization with Long Term Constraintscited by 6
  9. 2013A primal-dual hybrid gradient method for non-linear operators with applications to MRIcited by 5
  10. 2018Online convex optimization and no-regret learning: Algorithms, guarantees and applicationscited by 5
  11. 2018Running Primal-Dual Gradient Method for Time-Varying Nonconvex Problemscited by 4
  12. 2019Distributed Online Convex Optimization with Improved Dynamic Regretcited by 4
10 more
  1. 2019Online Gradient Descent for Linear Dynamical Systemscited by 4
  2. 2017Testing and non-linear preconditioning of the proximal point methodcited by 3
  3. 2020Predictive online optimisation with applications to optical flowcited by 2
  4. 2022A nonsmooth primal-dual method with interwoven PDE constraint solvercited by 2
  5. 2024Differential estimates for fast first-order multilevel nonconvex optimisationcited by 2
  6. 2018Acceleration and global convergence of a first-order primal--dual method for nonconvex problemscited by 1
  7. 2020Relaxed Gauss-Newton methods with applications to electrical impedance tomographycited by 1
  8. 2021Mumford-Shah regularization in electrical impedance tomography with complete electrode modelcited by 1
  9. 2022Bayesian Spatiotemporal Modeling for Inverse Problemscited by 1
  10. 2024Prediction techniques for dynamic imaging with online primal-dual methodscited by 1

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