Gridless 3D Recovery of Image Sources from Room Impulse Responses

TL;DR

This paper introduces a novel convex optimization method for accurately recovering the 3D positions and amplitudes of sparse sound sources in a room from limited microphone array measurements, advancing room acoustics analysis.

Contribution

It adapts super-resolution imaging techniques to the acoustic domain, enabling off-the-grid 3D source localization from room impulse responses using a convex linear inverse problem.

Findings

Achieves near-exact recovery of hundreds of sources in simulated environments.

Effective with a compact 32-channel spherical microphone array.

Performance analyzed under various noise, sampling, and array configurations.

Abstract

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.