Fully Reversing the Shoebox Image Source Method: From Impulse Responses to Room Parameters

TL;DR

This paper introduces an algorithm that fully recovers room and source parameters from shoebox model-based impulse responses, demonstrating near-perfect accuracy and outperforming existing methods in simulated environments.

Contribution

It presents the first algorithm capable of completely reversing the shoebox image source method to recover all room and source parameters from RIRs.

Findings

Near-exact parameter recovery in simulated experiments.

Estimation errors decrease with larger microphone arrays and higher sampling rates.

Outperforms baseline methods in accuracy and extrapolation capabilities.

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 first-order-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 2X2X2 to 10X10X5 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.