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Relatore: Prof. Marco Donatelli, Università dell’Insubria)

Titolo: Preconditioning Strategies for a Nested Primal-Dual Method for Image Deblurring

Abstract: 

Variational models for image deblurring problems typically consist of a smooth term and a potentially nonsmooth convex term. A common approach to solving these problems is using proximal gradient methods. Strategies such as variable metric methods have been introduced in the literature to accelerate the convergence of these first-order iterative algorithms.
In this talk, we show that, for image deblurring problems, the variable metric strategy can be reinterpreted as a right preconditioning method. Consequently, we explore an inexact left-preconditioned version of the same proximal gradient method. We prove the convergence of the new iteration to the minimum of a variational model where the norm of the data fidelity term depends on the preconditioner. The numerical results show that left and right preconditioning are comparable in terms of the number of iterations required to reach a prescribed tolerance, but left preconditioning needs much less CPU time, as it involves fewer evaluations of the preconditioner matrix compared to right preconditioning. The quality of the computed solutions with left and right preconditioning are comparable. Finally, we propose some nonstationary sequences of preconditioners that allow for fast and stable convergence to solve the variational problem with the classical L2-norm on the fidelity term.

L’attività si inquadra all’interno del progetto Startup GraphNet: modelli, computazione e stima per reti e grafi coordinato dalla Prof.ssa Silvia Columbu.