Preconditioned ADMM with nonlinear operator constraint
This work provides a new algorithmic tool for nonlinear inverse problems in imaging, though it is an incremental extension of existing methods.
The authors propose a preconditioned ADMM variant for convex optimization with nonlinear operator constraints, demonstrating its effectiveness on parallel MRI reconstruction.
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).