A direct variational approach to a problem arising in image reconstruction
type: Item
instance of: scholarly article
title: A direct variational approach to a problem arising in image reconstruction
zbMATH Open document ID: 1029.49037
DOI: 10.4171/IFB/72
author: Simon Masnou
author: Luigi Ambrosio
published in: Interfaces and Free Boundaries
publication date: 2003-06-29T00:00:00Z
review text: Summary: We consider a variational approach to the problem of recovering missing parts in a panchromatic digital image. Representing the image by a scalar function \(u\), we propose a model based on the relaxation of the energy \[ \int|\nabla u|\Biggl(\alpha+ \beta\Biggl|\text{div}{\nabla u\over|\nabla u|}\Biggr|^p\Biggr),\qquad\alpha, \beta> 0,\;p\geq 1, \] which takes into account the perimeter of the level sets of \(u\) as well as the \(L^p\) norm of the mean curvature along their boundaries. We investigate the properties of this variational model and the existence of minimizing functions in BV. We also address related issues for integral varifolds with generalized mean curvature in \(L^p\).
Mathematics Subject Classification ID: 49Q15
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 94A08
Mathematics Subject Classification ID: 68U10
zbMATH DE Number: 1941729
zbMATH Keywords: image processing
zbMATH Keywords: image reconstruction
zbMATH Keywords: relaxation
zbMATH Keywords: BV
zbMATH Keywords: integral varifolds
zbMATH Keywords: mean curvature
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/ifb/72
OpenAlex ID: W2013863892
description: scientific article; zbMATH DE number 1941729