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arXiv · 2509.08443

Hearing the Shape of a Cuboid Room Using Sparse Measure Recovery

Antoine Deleforge·Cédric Foy·Yannick Privat·Tom Sprunck
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Abstract

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.

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Antoine Deleforge, Cédric Foy, Yannick Privat, Tom Sprunck. 2025-09-10. Hearing the Shape of a Cuboid Room Using Sparse Measure Recovery. https://arxiv.org/abs/2509.08443

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