{"ID":2872535,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.08443","arxiv_id":"2509.08443","title":"Hearing the Shape of a Cuboid Room Using Sparse Measure Recovery","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.","short_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 config...","url_abs":"https://arxiv.org/abs/2509.08443","url_pdf":"https://arxiv.org/pdf/2509.08443v1","authors":"[\"Antoine Deleforge\",\"Cédric Foy\",\"Yannick Privat\",\"Tom Sprunck\"]","published":"2025-09-10T09:40:55Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}