State estimation with model reduction and shape variability: Application to biomedical problems
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2850 | |
dc.contributor.author | Galarce Marín, Felipe | |
dc.contributor.author | Lombardi, Damiano | |
dc.contributor.author | Mula, Olga | |
dc.date.accessioned | 2022-07-05T14:10:48Z | |
dc.date.available | 2022-07-05T14:10:48Z | |
dc.date.issued | 2021 | |
dc.description.abstract | We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems are posed on certain organs or portions of the body which inevitably involve morphological variations. If one wants to provide fast reconstruction methods, the algorithms must take into account the geometric variability. We develop and analyze a method which allows to take this variability into account without needing any a priori knowledge on a parametrization of the geometrical variations. For this, we rely on morphometric techniques involving Multidimensional Scaling, and couple them with reconstruction algorithms that make use of reduced model spaces pre-computed on a database of geometries. We prove the potential of the method on a synthetic test problem inspired from the reconstruction of blood flows and quantities of medical interest with Doppler ultrasound imaging. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9568 | |
dc.identifier.uri | https://doi.org/10.34657/8606 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2850 | |
dc.relation.issn | 2198-5855 | |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | |
dc.subject.other | inverse problems | eng |
dc.subject.other | shape variability | eng |
dc.subject.other | non-parametric domains | eng |
dc.subject.other | model reduction | eng |
dc.subject.other | multi-dimensional scaling | eng |
dc.subject.other | variational data assimilation | eng |
dc.title | State estimation with model reduction and shape variability: Application to biomedical problems | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 31 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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