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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.08443 |
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Table of Contents:
- This article explores a variant of Kac's famous problem, "Can one hear the shape of a drum?", by addressing a geometric inverse problem in acoustics. Our objective is to reconstruct the shape of a cuboid room using acoustic signals measured by microphones placed within the room. By examining this straightforward configuration, we aim to understand the relationship between the acoustic signals propagating in a room and its geometry. This geometric problem can be reduced to locating a finite set of acoustic point sources, known as image sources. We model this issue as a finite-dimensional optimization problem and propose a solution algorithm inspired by super-resolution techniques. This involves a convex relaxation of the finite-dimensional problem to an infinite-dimensional subspace of Radon measures. We provide analytical insights into this problem and demonstrate the efficiency of the algorithm through multiple numerical examples.