Joint Estimation of Common-Slope Decay Rates and Spatial Amplitudes Using Parameterized Nonnegative Matrix Factorization
Authors: Jeremy B. Bai, Filip Elvander, Sebastian J. Schlecht
Organizations: Multimedia Comms. & Signal Proc., Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany · Dept. of Information and Communications Engineering, Aalto University, Finland
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.
Figures & tables
Figure 1: Parameterized NMF for common-slope estimation. A fixed-frequency slice of all the stacked RIR spectrograms (in blue frame) forms a space–time power matrix Y . Its expected power V is factored into nonnegative spatial amplitudes A and exponential temporal features Φ with decay rates shared across RIRs. The right panel shows an individual observed response (in green frame) and the two fitted exponential decay components shown as straight lines in dB scale.
Figure 2: Excess IS loss (solid, left axis) and L2 RT-pair error (dashed, right axis) over SAGE iterations. Loss is shown relative to the lowest value attained by the displayed methods within 1000 iterations.
Figure 3: Amplitude-profiled observed-data IS loss and estimated RT trajectories from a pooled linear-fit initialization. The gray region is excluded due to parameter symmetry between the two RTs.
Figure 4: Estimated RTs for the room-to-hallway data. Blue and orange distinguish shorter and longer RTs.
Figure 5: Space–time component contributions near 2 kHz for the two configurations. The blending colors show the distribution of modeled variance shares between the decay components and noise floor. The dashed line marks the doorway between the room and hallway.
We present a simulation-trained, non-iterative estimator for Task A of the 1st DAFx Parameter Estimation Challenge. Each unnormalized plate-reverb impulse response is summarized by amplitude, spectral, and decay descriptors, and an ensemble of tree regressors estimates the six target parameters in one pass. Across two independent synthetic validation sets, the normalized models outperform the training-set mean and an earlier raw-regression baseline. On a shared set, the final ensemble also outperforms a single run of the official default PSO at substantially lower inference cost. Since the official labels are hidden, parameter accuracy is measured on simulator-matched data, and the released responses support only audio-side consistency checks. The estimator returns point estimates without uncertainty.
Minhui Lu, Joshua D. Reiss
Centre for Digital Music Queen Mary University of London London, United Kingdom
Image-source-method (ISM)-based room impulse response (RIR) simulation is a useful and physically interpretable tool for acoustic scene modeling, but full-order ISM becomes computationally expensive as the reflection order and room complexity increase. We propose a physics-guided framework for fast RIR simulation that preserves the geometric structure of ISM while learning to retain only acoustically important image-source paths during online traversal. To recover energy removed by pruning, the proposed PathRIR uses a lightweight compensation multilayer perceptron to predict the missing late-tail energy envelope and generate a compensation tail whose energy follows that envelope. Experiments on irregular 3D rooms show that PathRIR reduces image-source computation and improves runtime efficiency over a full-order ISM simulator, while achieving low waveform- and decay-related errors. Ablation results show that adding the compensation tail improves waveform fidelity and reduces energy-decay-curve error, reverberation-time error, and direct-to-reverberant-ratio error, with modest runtime overhead.
Shaoheng Xu, Chunyi Sun, Jihui Zhang +3
The Australian National University, Australia · The University of Queensland, Australia
Task B of the 1st DAFx Parameter Estimation Challenge requires estimating the frequencies, decay rates, gains, and number of modes in a dense plate-reverb impulse response. Weak and overlapping modes make sparse peak detection prone to severe undercounting. We train an ExtraTrees regressor on simulator-generated data to predict mode counts in four frequency bands. These counts define dense frequency grids, after which a differentiable all-pole resonator model refines decay and gain while keeping frequency fixed. On two separate synthetic validation sets, the system reduces a local challenge-style error by about 66% relative to the official default peak-picking baseline. The improvement is mainly associated with lower mode-count mismatch, while decay and gain remain the largest error sources. These findings support separating modal-density estimation from continuous parameter fitting.
Minhui Lu, Joshua D. Reiss
Centre for Digital Music Queen Mary University of London London, United Kingdom