Journal Article

PUBDB-2024-07394

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces

Burger, M.DESY* ; Schuster, T. ; Wald, A. (Corresponding author)

2024
Inst. Bristol [u.a.]

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Please use a persistent id in citations: doi:10.1088/1361-6420/ad5a35  doi:10.3204/PUBDB-2024-07394

Abstract: We consider time-dependent inverse problems in a mathematical setting using Lebesgue-Bochner spaces. Such problems arise when one aims to recover parameters from given observations where the parameters or the data depend on time. There are various important applications being subject of current research that belong to this class of problems. Typically inverse problems are ill-posed in the sense that already small noise in the data causes tremendous errors in the solution. In this article we present two different concepts of ill-posedness: temporally (pointwise) ill-posedness and uniform ill-posedness with respect to the Lebesgue-Bochner setting. We investigate the two concepts by means of a typical setting consisting of a time-depending observation operator composed by a compact operator. Furthermore we develop regularization methods that are adapted to the respective class of ill-posedness.

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Contributing Institute(s):

1. Computational Imaging (FS-CI)

Research Program(s):

1. 623 - Data Management and Analysis (POF4-623) (POF4-623)
2. SFB 1456 B06 - Kompensation von Bewegungen und Modellungenauigkeiten in der Nano-CT und lokalen Tomographie (B06) (502871779) (502871779)
3. GRK 2756 - GRK 2756: Das Zytoskelett als aktives System – von molekularen Wechselwirkungen zu zellulärer Biophysik (449750155) (449750155)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2024

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; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; National-Konsortium ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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