Generalized stability estimates in inverse transport theory

Bal, Guillaume; Jollivet, Alexandre

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.3934/ipi.2018003

URL permanente :

http://hdl.handle.net/20.500.12210/123247

Titre :

Generalized stability estimates in inverse transport theory

Auteur(s) :

Bal, Guillaume [Auteur]
Department of Applied Physics and Applied Mathematics [New York] [APAM]
Jollivet, Alexandre [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

Inverse Problems and Imaging

Pagination :

59-90

Éditeur :

AIMS American Institute of Mathematical Sciences

Date de publication :

2018

ISSN :

1930-8337

Mot(s)-clé(s) en anglais :

Linear transport
inverse problems
stability estimates
Wasserstein distance

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

Résumé en anglais : [en]

Inverse transport theory concerns the reconstruction of the absorption and scattering coefficients in a transport equation from knowledge of the albedo operator, which models all possible boundary measurements. Uniqueness ...
Lire la suite >Inverse transport theory concerns the reconstruction of the absorption and scattering coefficients in a transport equation from knowledge of the albedo operator, which models all possible boundary measurements. Uniqueness and stability results are well known and are typically obtained for errors of the albedo operator measured in the $L^1$ sense. We claim that such error estimates are not always very informative. For instance, arbitrarily small blurring and misalignment of detectors result in $O(1)$ errors of the albedo operator and hence in $O(1)$ error predictions on the reconstruction of the coefficients, which are not useful. This paper revisit such stability estimates by introducing a more forgiving metric on the measurements errors, namely the $1-$Wasserstein distances, which penalize blurring or misalignment by an amount proportional to the width of the blurring kernel or to the amount of misalignment. We obtain new stability estimates in this setting. We also consider the effect of errors, still measured in the $1-$Wasserstein distance, on the generation of the probing source. This models blurring and misalignment in the design of (laser) probes and allow us to consider a discretized sources. Under appropriate assumptions on the coefficients, we quantify the effect of such errors on the reconstructions.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Problèmes Inverses

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T17:49:53Z

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IP-wassertein-16.pdf
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1703.00691
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