第6回城西大学数理応用セミナー

日時: 2026年1月30日(金) 16:30 - 17:30

場所:城西大学紀尾井町キャンパス3号棟4階3401教室
https://www.josai.ac.jp/about/campus/kioicho/#2a3841cd
https://www.josai.ac.jp/access/kioicho/


城西大学数理応用セミナーホームページへ


懇親会：申し込みフォーム （締め切り1月23日（金））


講演者: Gesa Sarnighausen (Mathematical Sciences' at Georg-August-Universität Göttingen)

タイトル：Regularization of dynamic inverse problems with classical and data-driven methods

アブストラクト：
We investigate time-dependent inverse problems which arise when one aims to recover afunction from given observations where the function or the data depend on time. In this talk, we present two different approaches:
1. classical approach using Lebesgue-Bochner spaces in the function space setting
2. data-driven approach that incorporates the principle of causality
In the classical case, we first investigate geometrical properties of Lebesgue-Bochner spaces to implement Tikhonov regularization in these spaces using different regularities for time and space. Then, we develop a regularization algorithm to solve a variational minimization problem that penalizes the time-derivative in a Lebesgue-Bochner space. In the data-driven case, we are interested in incorporating the principle of causality, i.e. that an object at time t′ depends on its previous states t < t′ and is independent of future states t > t′ . We do that by solving a variational minimization problem for each time step using the information on the previous reconstructions. In particular, we train a spatial-temporal Transformer that gets the previous states as input and predicts the next output which then serves as a prior in the minimization problem for the next time step. We test all methods using the example of dynamic computerized tomography.