Lecture: A Bayesian approach to sparse inverse problems
Master data
Title: | A Bayesian approach to sparse inverse problems |
Description: | In this work, we study a Bayesian approach to the inverse problem of recovering an unknown sparse Radon measure u from a noisy observation y of its image through a known (possibly non-linear) forward G. We first define a prior measure on the space of Radon measures via point processes. We then study the well-posedness of the Bayesian inverse problem under a mild setting, which takes into account the above-mentioned prior measure. A sampling algorithm is proposed to compute an approximation of the associated posterior measure. Finally, we discuss a practical aspect of this Bayesian approach by considering the problem of identifying sound sources from pressure measurements. Here, the acoustics are modeled by the Helmholtz equation, and our goal is to get information about the strength and position of the sound sources. This is joint work with Barbara Kaltenbacher and Alexander Mozdzen. |
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Type: | Invited speaker |
Homepage: | http://math.ac.vn/conference/PDE2021/index.php?lang=vi |
Event: | International Conference on Differential Equations and Applications (Hanoi) |
Date: | 17.08.2022 |
lecture status: | stattgefunden (Präsenz) |
Participants
Phuoc Truong Huynh (internal) |
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Barbara Kaltenbacher (internal) |
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Alexander Mozdzen (internal) |
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Assignment
Organisation | Address | ||||
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Fakultät für Technische Wissenschaften
Institut für Mathematik
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AT - 9020 Klagenfurt am Wörthersee |
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Fakultät für Technische Wissenschaften
Institut für Statistik
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AT - 9020 Klagenfurt am Wörthersee |
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