Joint Estimation of Common-Slope Decay Rates and Spatial Amplitudes Using Parameterized Nonnegative Matrix Factorization

2026-10-04

AI Summary

This study addresses the challenging problem of jointly estimating the common-slope decay rate and spatial amplitude in room impulse responses. To this end, the joint estimation is formulated as a parameterized non-negative matrix factorization based on the Itakura–Saito divergence, which generates reverberation time curves without requiring backward integration. Furthermore, a contribution-weighted SAGE algorithm is introduced to significantly accelerate optimization convergence by emphasizing observation points with strong contributions. Experiments on synthetic data demonstrate that the proposed method accurately recovers separated decays while expediting loss convergence. Evaluations on measured data further reveal the spatiotemporal complementarity of shared components, thereby validating the effectiveness and practical utility of the proposed framework.

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.

Problem

• room impulse responses
• decay rate estimation
• reverberation time
• nonnegative matrix factorization
• coupled rooms

Innovation

• Parameterized Nonnegative Matrix Factorization
• Itakura-Saito Divergence
• Contribution-Weighted SAGE
• Reverberation Time Estimation
• Room Impulse Responses