Joint method finds decay rates and amplitudes from room impulse data
Joint Estimation of Common-Slope Decay Rates and Spatial Amplitudes Using Parameterized Nonnegative Matrix Factorization
Machine Learning
Summary
Measuring how sound fades away in a room helps understand its acoustics. The authors propose a new way to find detailed decay patterns at different frequencies using a math technique called nonnegative matrix factorization. Their method works directly on sound measurements without extra steps. Tests show it finds sound decay rates accurately and faster than older methods and can analyze real room sounds with overlapping echoes.
What this means in practice
- •For acoustic engineers: Create detailed frequency-dependent reverberation profiles from recorded room impulse responses to improve architectural acoustics design.
- •For audio software developers: Develop analysis tools that estimate sound decay parameters faster and more accurately from recordings without requiring extra processing steps.
Authors
Jeremy B. Bai, Filip Elvander, Sebastian J. Schlecht
Abstract
We formulate joint estimation of common-slope decay rates and amplitudes from room impulse responses (RIRs) as parameterized nonnegative matrix factorization with the Itakura--Saito divergence as the loss function (IS-NMF). Estimation at each short-time Fourier transform frequency bin produces detailed reverberation time (RT) curves directly from RIR powers with no backward integration needed. Standard space-alternating generalized expectation-maximization (SAGE) algorithm yields closed-form amplitude updates and a convex subproblem for each decay rate update. To accelerate estimation, we introduce contribution-weighted SAGE, which emphasizes observations where each component contributes strongly to the modeled power. Experiments with synthetic data show accurate recovery of well-separated decays and faster loss reduction than standard SAGE. Application to measured coupled-room RIRs yields frequency-dependent RT curves and reveals complementary space-time contributions of the shared decay components.