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Spatial Audio Signal Enhancement: A Multi-output MVDR Method in The Spherical Harmonic-domain

Huawei Zhang, Jihui Zhang, Huiyuan Sun, Prasanga Samarasinghe

arXiv:2409.03269v2eess.AS

TL;DR

Spatial audio enhancement seeks to suppress interference while preserving a desired sound field’s spatial cues, but existing methods can depend on impractical estimates or pre-training data. This paper uses ReHC-based multi-output SH-domain MVDR to extract desired SH coefficients; simulations report lower estimation error, higher SDR, and comparable NR than a beamforming-and-projection baseline.

  • Problem

    Spatial audio enhancement must separate a desired sound field from interference while preserving spatial cues, and existing methods can depend on accurate ATFs, accurate desired-signal PSD estimates, or pre-training data.

    Source: §I · p. 1

  • Method

    The method extends SH-domain MVDR to multiple beamformers and uses ReHC-based spatial constraints to extract desired SH coefficients directly from mixed recordings.

    Source: §I · pp. 1–2, §III · p. 2

  • Results

    Across 5 to −5 dB SNR, estimation error stayed about −19 dB and SDR about 22 dB, outperforming the baseline method; both methods maintained comparable NR above about 28 dB.

    Source: D. Performance Analysis over Varying… · p. 5

  • Takeaways & Limitations

    The method directly produces desired SH coefficients for reconstructing the desired sound field with spatial cues within the sweet area.

    Source: §I · p. 1, §V · p. 5

    The method requires a recording interval with only the desired source active and the summed interference-and-sensor-noise SH-domain PSD matrix in advance.

    Source: §III · p. 3

Abstract

from arXiv · show

Spatial audio signal enhancement aims to reduce interfering source contributions while preserving the desired sound field with its spatial cues. Existing methods generally rely on impractical assumptions (e.g. accurate estimations of impractical information) or have limited applicability. This paper presents a spherical harmonic (SH)-domain minimum variance distortionless response (MVDR)-based spatial signal enhancer using Relative Harmonic Coefficients (ReHCs) to extract clean SH coefficients from noisy recordings in reverberant environments. A simulation study shows the proposed method achieves lower estimation error, higher speech-distortion-ratio (SDR), and comparable noise reduction (NR) within the sweet area in a reverberant environment, compared to a beamforming-and-projection method as the baseline.

I. INTRODUCTION

Spatial audio enhancement separates a desired sound field from interference while preserving spatial cues, but existing approaches have practical limitations. This work develops a ReHC-based, multi-output SH-domain MVDR method.

I. INTRODUCTION

  • Spatial audio enhancement, also called ambisonic-to-ambisonic separation, preserves desired spatial cues while reducing interference and supports applications including sound-field decomposition, recording, reproduction, and spatial active noise control.The paper identifies these as applications of the technology.Source: §I · p. 1
  • Existing beamforming-and-projection methods can require accurate ATF estimates, Wiener filters need an accurately estimated desired-signal PSD matrix, and learning-based methods require pre-training data.Beamforming-and-projection methods also need a projection stage to reconstruct the desired sound field.Source: §I · p. 1
  • ReHCs are ratios of SH coefficients to the zeroth-order, zeroth-mode coefficient and can be estimated from received microphone signals’ SH-domain PSD matrices.Their potential for audio enhancement has not been fully studied.Source: §I · p. 1
  • The proposed multi-output SH-domain MVDR method extracts desired SH coefficients and directly outputs a sound field with spatial cues.It uses estimated ReHCs to construct spatial constraints, a more practical foreknowledge than estimated ATFs in.Source: §I · pp. 1–2

II. PROBLEM FORMULATION

The problem is to estimate desired SH coefficients from a mixture recorded by a spherical microphone array. The formulation represents the desired and interfering fields and sensor signals in the SH domain.

II. PROBLEM FORMULATION

  • Within the sweet area, the sound pressure is the sum of desired and interference fields, and microphone signals additionally include sensor noise.The desired source is assumed uncorrelated with the interference source, whose signal is assumed stable.Source: §II · p. 2
  • The microphone signals are transformed into mixed SH coefficients, decomposed into desired-field, interference-field, and sensor-noise coefficients.The representation uses L = (N + 1)^2 coefficients, indexed by SH order and mode.Source: §II · p. 2
  • The task is to extract desired SH coefficients from mixed SH coefficients obtained from the mixture recording.The scenario places desired and interfering sources outside a spherical sweet area in a reverberant room, with a concentric spherical microphone array.Source: §II · p. 2

III. PROPOSED MULTI-OUTPUT MVDR METHOD

The method extends SH-domain single-output MVDR to multiple outputs, using ReHC-based spatial constraints to estimate desired SH coefficients. Its operation requires specific recordings and noise statistics in advance.

III. PROPOSED MULTI-OUTPUT MVDR METHOD

  • The multi-output extension uses L beamformers, each estimating the desired SH coefficient at a corresponding order and mode.Together, the beamformers are represented as a single vector for design.Source: §III · p. 2
  • ReHC-based spatial constraints guide the beamformers to preserve desired SH coefficients while reducing interference and sensor-noise coefficients.The design uses the summed interference-and-sensor-noise SH-domain PSD matrix and desired-field ReHCs.Source: §III · p. 2
  • The estimated desired SH coefficients can be transformed back into sound-field pressure with spatial cues, although residual interference spatial cues may not be preserved.The inverse spherical harmonic transform reconstructs the estimated field from the output coefficients.Source: §III · p. 3
  • The proposed method requires a desired-source-only recording interval and the summed SH-domain PSD matrices of interference and sensor noise in advance.The paper notes that estimating a relative transfer matrix instead of ReHCs could waive the recording-interval requirement, but leaves that approach out of scope.Source: §III · p. 3

IV. SIMULATION AND RESULTS

The reverberant-room evaluation compares the proposed method with a beamforming-and-projection baseline, using a common SH-coefficient output for fair comparison.

  • The proposed method is evaluated against a leading-edge beamforming-and-projection method in a reverberant room.Source: §IV · p. 3
  • The baseline uses TF-domain single-output MVDR, estimated ATFs with nine-bin frequency smoothing, and projection to estimate desired microphone signals.Source: §IV · p. 3
  • For comparison, the baseline output is transformed into desired SH coefficients, as for the proposed method, and both fields are reconstructed with ISHT.Source: §IV · p. 3

A. Setup

The simulation uses a reverberant-room speech and washer-dryer-noise scenario, then evaluates the methods over the telephone bandwidth with at most third-order SH coefficients.

A. Setup

  • A simulated 5×6×4 m room with T60 = 0.2 s contains speech, washer-dryer interference, a 32-microphone spherical array, and sensor noise at 35 dB SSNR.The sweet-area and array radii are both 0.042 m; RIRs use the image-source method.Source: A. Setup · p. 3
  • Microphone signals undergo a 16384-sample STFT with 75% overlap, followed by SHT at each frequency using the corresponding maximum order Nk.Source: A. Setup · p. 3
  • Accurate simulated interference and sensor-noise PSD matrices are supplied to the baseline and proposed methods, respectively.Source: A. Setup · p. 3
  • Evaluation spans 300–3400 Hz, where speech information is concentrated; the Bessel Zero problem limits simulations to at most third-order SH coefficients.The passage notes that spherical-shell arrays can relieve the Bessel Zero problem.Source: A. Setup · p. 3

B. Performance Analysis Based on Sound Field Estimation Error

At 1500 Hz, both methods reconstruct a field similar to the true desired field within the sweet area, while the proposed method has lower estimation error.

B. Performance Analysis Based on Sound Field Estimation Error

C. Performance Analysis over Frequency

Across 300–3400 Hz, the proposed method with estimated ReHCs has lower error, higher SDR, and comparable NR to the baseline; more accurate ReHCs further improve error and SDR.

C. Performance Analysis over Frequency

  • The frequency analysis averages estimation error, SDR, and NR across 15 time frames and 107 observation points within the sweet area.Source: C. Performance Analysis over Frequency · p. 4
  • The estimated-ReHC method achieves lower error, higher SDR, and comparable NR than the baseline across 300–3400 Hz.At most chosen frequency bins, its estimation error is below −15 dB and SDR is above 15 dB; the figure plots the three metrics for estimated ReHCs, accurate ReHCs, and baseline.Source: C. Performance Analysis over Frequency · p. 4, Figure 3 · p. 4
  • More accurate ReHCs outperform estimated ReHCs on estimation error and SDR while achieving comparable NR, indicating sensitivity to ReHC estimation accuracy.The accurate ReHCs are obtained using white noise, which is described as more stable than speech across frequency bins.Source: C. Performance Analysis over Frequency · p. 4

D. Performance Analysis over Varying Reverberation Times and SNR Levels

Across reverberation times and SNR levels, the proposed method outperforms the baseline in estimation error and SDR while maintaining comparable noise reduction within the spherical sweet area. The evaluation averages results across 107 observation points and 15 time frames.

Evaluation Setup

Varying Reverberation Times

  • As T60 increased from 0 s to 0.4 s, both methods had higher estimation error, lower SDR, and lower NR; the proposed method consistently had lower error, higher SDR, and comparable NR.SNR was fixed at 0 dB; NR above 25 dB was considered effective enough.Source: D. Performance Analysis over Varying… · p. 5

Varying SNR Levels

  • About −19 dB estimation error and about 22 dB SDR were maintained across SNR levels, always outperforming the baseline, while both methods achieved comparable stable NR above about 28 dB.The SNR ranged from 5 dB to −5 dB, with T60 fixed at 0.2 s.Source: D. Performance Analysis over Varying… · p. 5

V. CONCLUSION

The paper proposes an SH-domain MVDR method to estimate the desired sound field from a spherical microphone-array mixture. Simulations show it can outperform baseline methods within the sweet area in a reverberant room, while analysis of how ReHC accuracy affects performance remains future work.

V. CONCLUSION

  • The proposed SH-domain MVDR method estimates the desired sound field from a mixture recorded with a spherical microphone array.Its cost function uses spatial constraints to extract desired SH coefficients and suppress interference and sensor-noise coefficients.Source: §V · p. 5
  • Simulation results show the proposed method can outperform baseline methods within the sweet area in a reverberant room.Source: §V · p. 5
  • The authors plan to theoretically analyze how ReHC accuracy influences the proposed method's performance.Source: §V · p. 5
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