A Preconditioned Version of a Nested Primal-Dual Algorithm for Image Deblurring
Stefano Aleotti, Marco Donatelli, Rolf Krause, Giuseppe Scarlato

TL;DR
This paper introduces a preconditioned variant of a nested primal-dual algorithm for image deblurring, demonstrating improved computational efficiency and comparable solution quality through theoretical convergence proofs and numerical experiments.
Contribution
It reinterprets variable metric strategies as preconditioning methods and develops an inexact left-preconditioned proximal gradient algorithm with proven convergence for image deblurring.
Findings
Left preconditioning reduces CPU time compared to right preconditioning.
Both preconditioning methods require similar iteration counts to reach convergence.
Proposed non-stationary preconditioner sequences enable fast, stable convergence.
Abstract
Variational models for image deblurring problems typically consist of a smooth term and a potentially non-smooth convex term. A common approach to solving these problems is using proximal gradient methods. To accelerate the convergence of these first-order iterative algorithms, strategies such as variable metric methods have been introduced in the literature. In this paper, we prove 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…
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Taxonomy
TopicsImage and Signal Denoising Methods · Advanced Image Processing Techniques · Advanced Image Fusion Techniques
