Unmatched Preconditioning of the Proximal Gradient Algorithm

Marion Savanier (1, 2) , Emilie Chouzenoux (1) , Jean-Christophe Pesquet (1) , Cyril Riddell (2)

1 OPIS - OPtimisation Imagerie et Santé
2 GE Healthcare - General Electric Medical Systems [Buc]

This work addresses the resolution of penalized least-squares problems using the proximal gradient algorithm (PGA). PGA can be accelerated by preconditioning strategies. However, typical effective choices of preconditioners may correspond to intricate matrices that are not easily inverted, leading to increased complexity in the computation of the proximity step. To relax these requirements, we propose an unmatched preconditioning approach where two metrics are used in the gradient step and the proximity step. We provide convergence conditions for this new iterative scheme and characterize its limit point. Simulations for tomographic image reconstruction from undersampled measurements show the benefits of our approach for various simple choices of metrics.

Mots clés: Computed tomography; Convergence analysis; Image reconstruction; Matrix approximation; Proximal methods

Domaines: Traitement du signal et de l'image [eess.SP]

Marion Savanier, Emilie Chouzenoux, Jean-Christophe Pesquet, Cyril Riddell. Unmatched Preconditioning of the Proximal Gradient Algorithm. IEEE Signal Processing Letters, 2022, 29, pp.1122-1126. ⟨10.1109/LSP.2022.3169088⟩. ⟨hal-03654146⟩