Existence and uniqueness of weak solutions for a new class of convex optimization problems related to image analysis
type: Item
instance of: scholarly article
title: Existence and uniqueness of weak solutions for a new class of convex optimization problems related to image analysis
zbMATH Open document ID: 1477.49025
DOI: 10.1155/2021/6691795
author: Anas Tiarimti Alaoui
author: Mostafa Jourhmane
published in: Journal of Mathematics
publication date: 2021-06-28T00:00:00Z
review text: Summary: This paper proposes a new anisotropic diffusion model in image restoration that is understood from a variational optimization of an energy functional. Initially, a family of new diffusion functions based on cubic Hermite spline is provided for optimal image denoising. After that, the existence and uniqueness of weak solutions for the corresponding Euler-Lagrange equation are proven in an appropriate functional space, and a consistent and stable numerical model is also shown. We complement this work by illustrating some experiments on different actual brain Magnetic Resonance Imaging (MRI) scans, showing the proposed model's impressive results.
Mathematics Subject Classification ID: 49K10
Mathematics Subject Classification ID: 94A08
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 7363816
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6691795
OpenAlex ID: W3155505389
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description: scientific article; zbMATH DE number 7363816