Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Determined blind source separation via modeling adjacent frequency band correlations in speech signals

Jianyu Wang, Shanzheng Guan, Zhengqiao Zhao, Nicolas Dobigeon, Jingdong Chen

TL;DR

The paper addresses the limitation of MBSS methods that assume independence across STFT frequency bins by exploiting strong correlations between adjacent frequency bands in speech. It introduces wsILRMA, a framework that combines a nonnegative matrix factorization source model with a Sinkhorn-divergence-based contrast to capture inter-frequency dependencies, aided by a fixed amplitude weight matrix to encode band correlations. The approach yields gradient-based updates for the transport-inspired auxiliary variables and NMF factors, and updates of the demixing matrices in an IVA-like fashion. Experimental results on simulated reverberant rooms show consistent SDR and SIR improvements over AuxIVA, ILRMA, and FastMNMF, with robustness to moderate reverberation and sensitivity to the inter-band weighting parameter $\eta$ in a practical range.

Abstract

Multichannel blind source separation (MBSS), which focuses on separating signals of interest from mixed observations, has been extensively studied in acoustic and speech processing. Existing MBSS algorithms, such as independent low-rank matrix analysis (ILRMA) and multichannel nonnegative matrix factorization (MNMF), utilize the low-rank structure of source models but assume that frequency bins are independent. In contrast, independent vector analysis (IVA) does not rely on a low-rank source model but rather captures frequency dependencies based on a uniform correlation assumption. In this work, we demonstrate that dependencies between adjacent frequency bins are significantly stronger than those between bins that are farther apart in typical speech signals. To address this, we introduce a weighted Sinkhorn divergence-based ILRMA (wsILRMA) that simultaneously captures these inter-frequency dependencies and models joint probability distributions. Our approach incorporates an inter-frequency correlation constraint, leading to improved source separation performance compared to existing methods, as evidenced by higher Signal-to-Distortion Ratios (SDRs) and Source-to-Interference Ratios (SIRs).

Determined blind source separation via modeling adjacent frequency band correlations in speech signals

TL;DR

The paper addresses the limitation of MBSS methods that assume independence across STFT frequency bins by exploiting strong correlations between adjacent frequency bands in speech. It introduces wsILRMA, a framework that combines a nonnegative matrix factorization source model with a Sinkhorn-divergence-based contrast to capture inter-frequency dependencies, aided by a fixed amplitude weight matrix to encode band correlations. The approach yields gradient-based updates for the transport-inspired auxiliary variables and NMF factors, and updates of the demixing matrices in an IVA-like fashion. Experimental results on simulated reverberant rooms show consistent SDR and SIR improvements over AuxIVA, ILRMA, and FastMNMF, with robustness to moderate reverberation and sensitivity to the inter-band weighting parameter in a practical range.

Abstract

Multichannel blind source separation (MBSS), which focuses on separating signals of interest from mixed observations, has been extensively studied in acoustic and speech processing. Existing MBSS algorithms, such as independent low-rank matrix analysis (ILRMA) and multichannel nonnegative matrix factorization (MNMF), utilize the low-rank structure of source models but assume that frequency bins are independent. In contrast, independent vector analysis (IVA) does not rely on a low-rank source model but rather captures frequency dependencies based on a uniform correlation assumption. In this work, we demonstrate that dependencies between adjacent frequency bins are significantly stronger than those between bins that are farther apart in typical speech signals. To address this, we introduce a weighted Sinkhorn divergence-based ILRMA (wsILRMA) that simultaneously captures these inter-frequency dependencies and models joint probability distributions. Our approach incorporates an inter-frequency correlation constraint, leading to improved source separation performance compared to existing methods, as evidenced by higher Signal-to-Distortion Ratios (SDRs) and Source-to-Interference Ratios (SIRs).

Paper Structure

This paper contains 12 sections, 20 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Signal Model and Problem Formulation
  3. Proposed Model and Source Separation algorithm
  4. Illustration of inter-band correlation
  5. Contrast function based on Optimal spectral transport
  6. The weighted Sinkhorn divergence-based ILRMA (wsILRMA)
  7. Simulation results
  8. Simulation configuration
  9. Algorithm parameters
  10. Compared algorithms and performance metrics
  11. Simulation results and discussions
  12. Conclusion

Figures (4)

  • Figure 1: The magnitude of pairwise normalized correlation coefficients between STFT frequency bins of a speech signal. The sampling rate is $8$ kHz, the frame length is $16$ ms ($128$ points), the FFT length is $128$, and the overlap is $50\%$
  • Figure 2: Visualization of the fixed amplitude weights $\mathbf{U}$ (a) and $-\log\mathbf{U}$ (b). The FFT length is $1024$ points. $\mathbf{U}$ reflect similar inter-band dependencies as the inter-band correlation coefficients.
  • Figure 3: Simulation results for MBSS in Condition 1. Average SIR (left) and SDR (right) performance with varying amplitude weighting parameter $\eta$ under different reverberation conditions. Note that the x-axis in the logarithmic scale. The bands show the $95\%$ confidence interval around the mean. The dashed lines indicate the mean performance for comparison methods.
  • Figure 4: Simulation results for MBSS in Condition 2. Average SIR (left) and SDR (right) performance with varying amplitude weighting parameter $\eta$ under different reverberation conditions. Note that the x-axis in the logarithmic scale. The bands show the $95\%$ confidence interval around the mean. The dashed lines indicate the mean performance for comparison methods.