
State estimation with nonlinear reduced models. Application to the reconstruction of blood flows with Doppler ultrasound images
Galarce, Felipe; Gerbeau, Jean-Frédéric; Lombardi, Damiano; Mula, Olga (2019), State estimation with nonlinear reduced models. Application to the reconstruction of blood flows with Doppler ultrasound images. https://basepub.dauphine.fr/handle/123456789/20342
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Type
Document de travail / Working paperExternal document link
https://hal.archives-ouvertes.fr/hal-02403686Date
2019Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-DauphinePublished in
Paris
Pages
19
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Show full item recordAuthor(s)
Galarce, FelipeLaboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Gerbeau, Jean-Frédéric

Inria Siège
Lombardi, Damiano
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Mula, Olga

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
Over the past years, several fast reconstruction algorithms based on reduced models have been proposed to address the state estimation problem of approximating an unknown function u of a Hilbert space V from measurement observations. Most strategies are however based on linear mappings where the reduced model is built a priori and independently of the observation space and the measurements. In this work we explore some nonlinear extensions that take these elements into account in the construction of the basis. The methodology is applied to the reconstruction of 3D blood flows from Doppler ultrasound images. The example not only shows the good performance of the nonlinear methods, but it also illustrates the potential of the methodology in medicine as tool to process and interpret data in a systematic manner which could help to build more robust and individualized diagnostics.Subjects / Keywords
Doppler ultrasound imagesRelated items
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