Preconditioned ADMM with nonlinear operator constraint
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Peer-reviewed
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Authors
Benning, Martin
Knoll, Florian
Schonlieb, Carola-Bibiane
Valkonen, Tuomo
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).
Description
This is the author accepted manuscript. The final version is available from Springer via https://doi.org/10.1007/978-3-319-55795-3_10.
Keywords
ADMM, primal-dual, nonlinear inverse problems, parallel MRI, proximal point method, operator splitting, iterative Bregman method
Journal Title
IFIP Advances in Information and Communication Technology
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494
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Springer
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Sponsorship
MB, CS and TV acknowledge EPSRC grant EP/M00483X/1. FK ackowledges National Institutes of Health grant NIH P41 EB017183.