Preconditioned ADMM with Nonlinear Operator Constraint

  • Martin Benning
  • Florian Knoll
  • Carola-Bibiane Schönlieb
  • Tuomo Valkonen
Conference paper
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 494)

Abstract

We are presenting a modification of the well-known Alternating Direction Method of Multipliers (ADMM) algorithm with additional preconditioning that aims at solving convex optimisation problems with nonlinear operator constraints. Connections to the recently developed Nonlinear Primal-Dual Hybrid Gradient Method (NL-PDHGM) are presented, and the algorithm is demonstrated to handle the nonlinear inverse problem of parallel Magnetic Resonance Imaging (MRI).

Keywords

ADMM Primal-dual Nonlinear inverse problems Parallel MRI Proximal point method Operator splitting Iterative Bregman method 

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Copyright information

© IFIP International Federation for Information Processing 2016

Authors and Affiliations

  • Martin Benning
    • 1
  • Florian Knoll
    • 2
  • Carola-Bibiane Schönlieb
    • 1
  • Tuomo Valkonen
    • 3
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK
  2. 2.Center for Advanced Imaging, Innovation and ResearchNew York UniversityNew YorkUSA
  3. 3.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK

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