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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


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ISSN
1569-3945
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Volume 16, Issue 2 (Jan 2008)

Issues

The multidimensional refinement indicators algorithm for optimal parameterization

H. Ben Ameur
  • FSB and ENIT-LAMSIN, University of Tunis, BP 37, Le Belvédère, 1002 Tunis, Tunisia. Email: hbenameur@yahoo.ca
  • Other articles by this author:
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/ F. Clément
  • Projet Estime, INRIA-Rocquencourt, Domaine de Voluceau, BP 105, 78153 Le Chesnay cedex, France. Email: Francois.Clement@inria.fr
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ P. Weis
  • Projet Cristal, INRIA-Rocquencourt, Domaine de Voluceau, BP 105, 78153 Le Chesnay cedex, France. Email: Pierre.Weis@inria.fr
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/ G. Chavent
  • Projet Estime, INRIA-Rocquencourt, Domaine de Voluceau, BP 105, 78153 Le Chesnay cedex, France. Email: Guy.Chavent@inria.fr
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  • De Gruyter OnlineGoogle Scholar
Published Online: 2008-05-09 | DOI: https://doi.org/10.1515/JIIP.2008.008

Abstract

The estimation of distributed parameters in a partial differential equation (PDE) from measures of the solution of the PDE may lead to underdetermination problems. The choice of a parameterization is a frequently used way of adding a priori information by reducing the number of unknowns according to the physics of the problem. The refinement indicators algorithm provides a fruitful adaptive parameterization technique that parsimoniously opens the degrees of freedom in an iterative way. We present a new general form of the refinement indicators algorithm that is applicable to the estimation of distributed multidimensional parameters in any PDE. In the linear case, we state the relationship between the refinement indicator and the decrease of the usual least-squares data misfit objective function. We give numerical results in the simple case of the identity model, and this application reveals the refinement indicators algorithm as an image segmentation technique.

Key words.: Inverse problem; parameter estimation; optimal parameterization; image segmentation; functional programming

About the article

Received: 2006-10-10

Published Online: 2008-05-09

Published in Print: 2008-03-01


Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2008.008.

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[1]
H. Ben Ameur, G. Chavent, F. Cheikh, F. Clément, V. Martin, and J. E. Roberts
Inverse Problems in Science and Engineering, 2017, Page 1
[2]
H. Ben Ameur, G. Chavent, F. Clément, and P. Weis
Inverse Problems in Science and Engineering, 2011, Volume 19, Number 5, Page 577

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