The Multi-Dimensional Refinement Indicators Algorithm for Optimal Parameterization

Abstract : The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual 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 multi-dimensional 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.
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Journal articles
Journal of Inverse and Ill-posed Problems, De Gruyter, 2008, 16 (2), pp.107-126. <10.1515/JIIP.2008.008>
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Submitted on : Wednesday, January 16, 2008 - 1:39:56 PM
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Hend Ben Ameur, François Clément, Pierre Weis, Guy Chavent. The Multi-Dimensional Refinement Indicators Algorithm for Optimal Parameterization. Journal of Inverse and Ill-posed Problems, De Gruyter, 2008, 16 (2), pp.107-126. <10.1515/JIIP.2008.008>. <inria-00079668v6>

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