Journal Article

PUBDB-2026-01186

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Regularization for time-dependent inverse problems: geometry of Lebesgue–Bochner spaces and algorithms

Sarnighausen, G. ; Hohage, T. ; Burger, M.DESY* ; Hauptmann, A. ; Wald, A. (Corresponding author)

2026
Inst. Bristol [u.a.]

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Please use a persistent id in citations: doi:10.1088/1361-6420/ae30f9  doi:10.3204/PUBDB-2026-01186

Abstract: We consider time-dependent inverse problems in a mathematical setting using Lebesgue–Bochner spaces. Such problems arise when one aims to recover a function from given observations where the function or the data depend on time. Lebesgue–Bochner spaces allow to easily incorporate the different nature of time and space.In this manuscript, we present two different regularization methods in Lebesgue–Bochner spaces:a. classical Tikhonov regularization in Banach spaces,b. temporal variational regularization by penalizing the time-derivative.In the first case, we additionally investigate geometrical properties of Lebesgue–Bochner spaces. This particularly includes the calculation of the duality mapping and it is shown that these spaces are smooth of power type. The resulting Tikhononv regularization in Lebesgue–Bochner spaces is implemented using different regularities for time and space. Both methods are tested and evaluated for dynamic computerized tomography.

Note: cc-by

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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. DFG project G:(GEPRIS)432680300 - SFB 1456: Mathematik des Experiments: Die Herausforderung indirekter Messungen in den Naturwissenschaften (432680300) (432680300)
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 2026

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Database coverage:
; ; ; 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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