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State estimation with nonlinear reduced models. Application to the reconstruction of blood flows with Doppler ultrasound images

Abstract : 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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-02403686
Contributor : Olga Mula <>
Submitted on : Tuesday, December 10, 2019 - 11:01:41 PM
Last modification on : Wednesday, September 23, 2020 - 4:30:19 AM

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  • HAL Id : hal-02403686, version 1
  • ARXIV : 1904.13367

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Felipe Galarce, Jean-Frédéric Gerbeau, Damiano Lombardi, Olga Mula. State estimation with nonlinear reduced models. Application to the reconstruction of blood flows with Doppler ultrasound images. 2019. ⟨hal-02403686⟩

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