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An automatic pixel-wise multi-penalty approach to image restoration
Version 1
: Received: 2 October 2023 / Approved: 3 October 2023 / Online: 4 October 2023 (07:36:11 CEST)
A peer-reviewed article of this Preprint also exists.
Bortolotti, V.; Landi, G.; Zama, F. An Automatic Pixel-Wise Multi-Penalty Approach to Image Restoration. J. Imaging 2023, 9, 249. Bortolotti, V.; Landi, G.; Zama, F. An Automatic Pixel-Wise Multi-Penalty Approach to Image Restoration. J. Imaging 2023, 9, 249.
Abstract
This work tackles the problem of image restoration, a crucial task in many fields of applied sciences, focusing on removing degradation caused by blur and noise during the acquisition process. Drawing inspiration from the multi-penalty approach based on the Uniform Penalty principle introduced in [Bortolotti et al. arXiv.math.NA/2309.14163], we develop here a new image restoration model and an iterative algorithm for its effective solution.
The model incorporates pixel-wise regularization terms and establishes a rule for parameters selection, aiming to restore images through the solution of a sequence of constrained optimization problems. To achieve this, we present a modified version of the Newton Projection method, adapted to multi-penalty scenarios, and prove its convergence. Numerical experiments demonstrate the efficacy of the method in eliminating noise and blur while preserving the image edges.
Keywords
Multi-Penalty regularization; Image Restoration; Uniform Penalty Principle
Subject
Computer Science and Mathematics, Computer Vision and Graphics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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