Space-dependent Sobolev gradients as a regularization for inverse radiative transfer problems
type: Item
instance of: scholarly article
title: Space-dependent Sobolev gradients as a regularization for inverse radiative transfer problems
zbMATH Open document ID: 1400.65065
DOI: 10.1155/2016/3543571
author: F. Dubot
author: D. Le Hardy
author: B. Rousseau
author: D. Rousse
author: Y. Favennec
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: Diffuse optical tomography problems rely on the solution of an optimization problem for which the dimension of the parameter space is usually large. Thus, gradient-type optimizers are likely to be used, such as the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, along with the adjoint-state method to compute the cost function gradient. Usually, the \(L_2\)-inner product is chosen within the extraction procedure (i.e., in the definition of the relationship between the cost function gradient and the directional derivative of the cost function) while alternative inner products that act as regularization can be used. This paper presents some results based on space-dependent Sobolev inner products and shows that this method acts as an efficient low-pass filter on the cost function gradient. Numerical results indicate that the use of Sobolev gradients can be particularly attractive in the context of inverse problems, particularly because of the simplicity of this regularization, since a single additional diffusion equation is to be solved, and also because the quality of the solution is smoothly varying with respect to the regularization parameter.
Mathematics Subject Classification ID: 65R32
Mathematics Subject Classification ID: 92C55
zbMATH DE Number: 6953068
Wikidata QID: Q59130882
describes a project that uses: FreeFem++
describes a project that uses: L-BFGS
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/3543571
OpenAlex ID: W2316901784
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description: scientific article; zbMATH DE number 6953068