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

2024-05-06

IEEE Transactions on Audio, Speech, and Language Processing

AI Summary

This work addresses the inverse problem of the Image Source Method (ISM) for shoebox-shaped rooms: jointly estimating 18 physical parameters—3D source location, room dimensions along three axes, six-degree-of-freedom pose (3D translation and 3D rotation), and absorption coefficients of all six walls—from multichannel room impulse responses (RIRs) with high accuracy. We provide the first theoretical proof and practical realization of global identifiability for the ISM inverse problem. Our method introduces a novel paradigm comprising grid-free image-source localization, geometric recovery of room coordinate axes, and first-order reflection time-of-arrival identification, integrating reflection-path modeling, geometric constraint optimization, and low-pass RIR parameterization. Evaluated in cubic rooms of 2–10 m, using a 32-element spherical microphone array and 16-kHz sampling, our approach achieves near-zero parameter estimation error and significantly outperforms state-of-the-art methods in RIR extrapolation.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services

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 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.

Problem

• Recovers 18 input parameters from room impulse responses.
• Uses gridless image source localization for room parameter estimation.
• Achieves near-exact recovery with a 32-element microphone array.

Innovation

• Reverses shoebox ISM to recover room parameters
• Uses gridless image source localization technique
• Identifies first-order reflections for accurate recovery