Gridless 3D Recovery of Image Sources From Room Impulse Responses

Abstract

We present an algorithm that fully reverses the shoebox image source method (ISM), a popular and widely used room impulse response (RIR) simulator for cuboid rooms introduced by Allen and Berkley in 1979. More precisely, given a discrete multichannel RIR generated by the shoebox ISM for a microphone array of known geometry, the algorithm reliably recovers the 18 input parameters. These are the 3D source position, the 3 dimensions of the room, the 6-degrees-of-freedom room translation and orientation, and an absorption coefficient for each of the 6 room boundaries. The approach builds on a recently proposed gridless image source localization technique combined with new procedures for room axes recovery and firstorder-reflection identification. Extensive simulated experiments reveal that near-exact recovery of all parameters is achieved for a 32-element, 8.4-cm-wide spherical microphone array and a sampling rate of 16 kHz using fully randomized input parameters within rooms of size 2×2×2 to 10×10×5 meters. Estimation errors decay towards zero when increasing the array size and sampling rate. The method is also shown to strongly outperform a known baseline, and its ability to extrapolate RIRs at new positions is demonstrated. Crucially, the approach is strictly limited to low-passed discrete RIRs simulated using the vanilla shoebox ISM. Nonetheless, it represents to our knowledge the first algorithmic demonstration that this difficult inverse problem is in-principle fully solvable over a wide range of configurations.

Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application

“…For convex methods solving (5), other than Sliding Frank-Wolfe, there is a whole body of works [10,17,33] based on solving the dual problem, which poses difficulties in high dimensions, even if we can cite recent advances using methods with adaptive refining of a grid [23]. Concerning Sliding Frank-Wolfe, in the context of acoustic impulse response estimation, the idea of performing a single descent over all parameters after a greedy initialization is also used in [36].…”