An Automatic Pixel-Wise Multi-Penalty Approach to Image Restoration

Author:

Bortolotti Villiam1ORCID,Landi Germana2ORCID,Zama Fabiana2ORCID

Affiliation:

1. Department of Civil, Chemical, Environmental, and Materials Engineering, University of Bologna, 40131 Bologna, Italy

2. Department of Mathematics, University of Bologna, 40127 Bologna, Italy

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, discussed in previous work, here we develop 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 parameter 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.

Publisher

MDPI AG

Subject

Electrical and Electronic Engineering,Computer Graphics and Computer-Aided Design,Computer Vision and Pattern Recognition,Radiology, Nuclear Medicine and imaging

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