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Article Dans Une Revue IEEE Signal Processing Letters Année : 2022

Gridless 3D Recovery of Image Sources from Room Impulse Responses

Résumé

Given a sound field generated by a sparse distribution of impulse image sources, can the continuous 3D positions and amplitudes of these sources be recovered from discrete, bandlimited measurements of the field at a finite set of locations, e.g., a multichannel room impulse response? Borrowing from recent advances in super-resolution imaging, it is shown that this nonlinear, non-convex inverse problem can be efficiently relaxed into a convex linear inverse problem over the space of Radon measures in R3. The linear operator introduced here stems from the fundamental solution of the free-field inhomogenous wave equation combined with the receivers' responses. An adaptation of the Sliding Frank-Wolfe algorithm is proposed to numerically solve the problem off-the-grid, i.e., in continuous 3D space. Simulated experiments show that the approach achieves near-exact recovery of hundreds of image sources using an arbitrarily placed compact 32-channel spherical microphone array in random rectangular rooms. The impact of noise, sampling rate and array diameter on these results is also examined.
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Dates et versions

hal-03763838 , version 1 (29-08-2022)
hal-03763838 , version 2 (05-12-2022)

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Tom Sprunck, Antoine Deleforge, Yannick Privat, Cédric Foy. Gridless 3D Recovery of Image Sources from Room Impulse Responses. IEEE Signal Processing Letters, 2022, ⟨10.1109/LSP.2022.3224682⟩. ⟨hal-03763838v2⟩
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