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

arXiv: https://arxiv.org/abs/2610.05549 · HTML: https://mlsanity.com/paper/2610.05549/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 19 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 2 of 2)

- [Truncated Variational Expectation Maximization](https://mlsanity.com/paper/1610.03113/) (2016)
- [Neural network for multi-exponential sound energy decay analysis](https://mlsanity.com/paper/2205.09644/) (2022)

## Abstract (arXiv)

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.