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.
Keywords
Publication details
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Cite this article
APA 7
Bai, J. B., Elvander, F., & Schlecht, S. J. (2026). Joint Estimation of Common-Slope Decay Rates and Spatial Amplitudes Using Parameterized Nonnegative Matrix Factorization. https://omanscience.com/en/articles/joint-estimation-of-common-slope-decay-rates-and-spatial-amplitudes-using-parameterized-nonnegative-matrix-factorization
MLA 9
Bai, Jeremy B., et al. "Joint Estimation of Common-Slope Decay Rates and Spatial Amplitudes Using Parameterized Nonnegative Matrix Factorization." https://omanscience.com/en/articles/joint-estimation-of-common-slope-decay-rates-and-spatial-amplitudes-using-parameterized-nonnegative-matrix-factorization.
Chicago (author–date)
Bai, Jeremy B., Filip Elvander, and Sebastian J. Schlecht. 2026. "Joint Estimation of Common-Slope Decay Rates and Spatial Amplitudes Using Parameterized Nonnegative Matrix Factorization." https://omanscience.com/en/articles/joint-estimation-of-common-slope-decay-rates-and-spatial-amplitudes-using-parameterized-nonnegative-matrix-factorization.
Harvard
Bai, J. B., Elvander, F. and Schlecht, S. J. (2026) 'Joint Estimation of Common-Slope Decay Rates and Spatial Amplitudes Using Parameterized Nonnegative Matrix Factorization', Available at: https://omanscience.com/en/articles/joint-estimation-of-common-slope-decay-rates-and-spatial-amplitudes-using-parameterized-nonnegative-matrix-factorization.
Vancouver
Bai JB, Elvander F, Schlecht SJ. Joint Estimation of Common-Slope Decay Rates and Spatial Amplitudes Using Parameterized Nonnegative Matrix Factorization. https://omanscience.com/en/articles/joint-estimation-of-common-slope-decay-rates-and-spatial-amplitudes-using-parameterized-nonnegative-matrix-factorization
IEEE
J. B. Bai, F. Elvander, and S. J. Schlecht, "Joint Estimation of Common-Slope Decay Rates and Spatial Amplitudes Using Parameterized Nonnegative Matrix Factorization," https://omanscience.com/en/articles/joint-estimation-of-common-slope-decay-rates-and-spatial-amplitudes-using-parameterized-nonnegative-matrix-factorization.