Similarity Metrics for Late Reverberation

Companion repository for the paper 'Similarity Metrics for Late Reverberation' presented at ASILOMAR 2024.
Pre-print available on Arxiv [1]

The objective results presented in this study have been computed on the dataset of impulse responses from variable acoustics room Arni at Aalto Acoustic Labs [2] available on Zenodo

This repository contains the code used for

• Data pre-processing and sub-sampling (get_subset_rirs.py, get_mixing_time.py)

• Evaluating similarity between RIRs using

  • proposed similarity metrics $\mathcal{L}_{\textrm{PC}}$ and $\mathcal{L}_{\textrm{EDC}}$
  • baselines $\mathcal{L}_{\textrm{MSS}}$ [3] and $\mathcal{L}_{\textrm{ESR}}$

  by analyzing differences in absorption confitions (numclosed_effect.py) and microphone location (mic_position_effect.py)

• Evaluating the evolution of metrics on gradual differences (smoothness.py)

• Plotting (./plotting, uses matlab)

Introduction

Accurate tuning of parametric artificial reverberators relies heavily on the choice of cost function, yet common audio similarity metrics do not account for the unique statistical properties of late room reverberation. We introduce two novel similarity metrics specifically designed for this purpose, which outperform existing metrics on a dataset of measured room impulse responses (RIRs). We propose a methodology that involves datasets like the Arni dataset to evaluate the performance of these loss functions to capture statistical differences between various absorption configurations, as well as their robustness to changes in microphone position.

Proposed Similarity Metrics

Averaged power convergence

Distance on the time-frequency representation:

$\mathcal{L}_{\textrm{PC}} = \left\lVert \frac{| H(t, f)|^2 * W - |\hat{H}(t, f) |^2 * W}{(| H(t, f) |^2 * W) (| \hat{H}(t, f) |^2 * W)} \right\rVert_{\textrm{F}}$

The squared magnitude short-time Fourier transform of the RIR $h(t)$, $\lvert H(t, f) \rvert^2$, is smoothed by convolving it with a 2D Hann window $W$, to mitigate short-term fluctuations.

Energy decay convergence

Convergence of the energy level over time and frequency:

$\mathcal{L}_{\text{EDC}} = \frac{1}{|\mathcal{C}|}\sum_{f_{\textrm{c}} \in \mathcal{C}} \frac{\sum_{t=0}^L \left( \varepsilon_{\textrm{dB}}(t; f_\textrm{c}) - \hat{\varepsilon}_{\textrm{dB}}(t; f_\textrm{c}) \right)^2}{\sum_{t=0}^L \varepsilon_{\textrm{dB}}^2(t; f_\textrm{c})} $

The energy decay curve (EDC) at each frequency band $\textrm{c} \in \mathcal{C}$, $\varepsilon_{\textrm{dB}}(t; f_\textrm{c})\,$, is normalized to 0 dB to avoid emphasizing differences in noise level.

Dataset of measured RIRs

We used a dataset of measured RIRs from a variable acoustics room [2], pre-processed to remove direct and early reflections, and segmented into 11 subsets based on the absorption configuration. For each partition, we randomly selected 25RIRs, 5RIRs for each of the 5 receiver positions.

References

[1] Dal Santo, G., Prawda, K., Schlecht, S. J., & Välimäki, V. (2024). Similarity Metrics For Late Reverberation. arXiv preprint arXiv:2408.14836.
[2] K. Prawda, S. J. Schlecht, and V. Välimäki, “Calibrating the Sabine and Eyring formulas,” J. Acoust. Soc. Am., 2022 [3] R. Yamamoto, E. Song, and J.-M. Kim, “Parallel WaveGAN: A fast waveform generation model based on generative adversarial networks with multi-resolution spectrogram,” in Proc. IEEE ICASSP, 2020.