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Speech Enhancement with MVDR Beamforming

Author: Zhaoheng Ni

1. Overview

This is a tutorial on applying Minimum Variance Distortionless Response (MVDR) beamforming to estimate enhanced speech with TorchAudio.


import torch
import torchaudio
import torchaudio.functional as F


2. Preparation

2.1. Import the packages

First, we install and import the necessary packages.

mir_eval, pesq, and pystoi packages are required for evaluating the speech enhancement performance.

# When running this example in notebook, install the following packages.
# !pip3 install mir_eval
# !pip3 install pesq
# !pip3 install pystoi

from pesq import pesq
from pystoi import stoi
import mir_eval

import matplotlib.pyplot as plt
from IPython.display import Audio
from torchaudio.utils import download_asset

2.2. Download audio data

The multi-channel audio example is selected from ConferencingSpeech dataset.

The original filename is


which was generated with:

  • SSB07200001.wav from AISHELL-3 (Apache License v.2.0)

  • noise-sound-bible-0038.wav from MUSAN (Attribution 4.0 International — CC BY 4.0)

SAMPLE_CLEAN = download_asset("tutorial-assets/mvdr/clean_speech.wav")
SAMPLE_NOISE = download_asset("tutorial-assets/mvdr/noise.wav")
  0%|          | 0.00/0.98M [00:00<?, ?B/s]
100%|##########| 0.98M/0.98M [00:00<00:00, 155MB/s]

  0%|          | 0.00/1.95M [00:00<?, ?B/s]
100%|##########| 1.95M/1.95M [00:00<00:00, 232MB/s]

2.3. Helper functions

def plot_spectrogram(stft, title="Spectrogram", xlim=None):
    magnitude = stft.abs()
    spectrogram = 20 * torch.log10(magnitude + 1e-8).numpy()
    figure, axis = plt.subplots(1, 1)
    img = axis.imshow(spectrogram, cmap="viridis", vmin=-100, vmax=0, origin="lower", aspect="auto")
    plt.colorbar(img, ax=axis)

def plot_mask(mask, title="Mask", xlim=None):
    mask = mask.numpy()
    figure, axis = plt.subplots(1, 1)
    img = axis.imshow(mask, cmap="viridis", origin="lower", aspect="auto")
    plt.colorbar(img, ax=axis)

def si_snr(estimate, reference, epsilon=1e-8):
    estimate = estimate - estimate.mean()
    reference = reference - reference.mean()
    reference_pow = reference.pow(2).mean(axis=1, keepdim=True)
    mix_pow = (estimate * reference).mean(axis=1, keepdim=True)
    scale = mix_pow / (reference_pow + epsilon)

    reference = scale * reference
    error = estimate - reference

    reference_pow = reference.pow(2)
    error_pow = error.pow(2)

    reference_pow = reference_pow.mean(axis=1)
    error_pow = error_pow.mean(axis=1)

    si_snr = 10 * torch.log10(reference_pow) - 10 * torch.log10(error_pow)
    return si_snr.item()

def generate_mixture(waveform_clean, waveform_noise, target_snr):
    power_clean_signal = waveform_clean.pow(2).mean()
    power_noise_signal = waveform_noise.pow(2).mean()
    current_snr = 10 * torch.log10(power_clean_signal / power_noise_signal)
    waveform_noise *= 10 ** (-(target_snr - current_snr) / 20)
    return waveform_clean + waveform_noise

def evaluate(estimate, reference):
    si_snr_score = si_snr(estimate, reference)
    ) = mir_eval.separation.bss_eval_sources(reference.numpy(), estimate.numpy(), False)
    pesq_mix = pesq(SAMPLE_RATE, estimate[0].numpy(), reference[0].numpy(), "wb")
    stoi_mix = stoi(reference[0].numpy(), estimate[0].numpy(), SAMPLE_RATE, extended=False)
    print(f"SDR score: {sdr[0]}")
    print(f"Si-SNR score: {si_snr_score}")
    print(f"PESQ score: {pesq_mix}")
    print(f"STOI score: {stoi_mix}")

3. Generate Ideal Ratio Masks (IRMs)

3.1. Load audio data

waveform_clean, sr = torchaudio.load(SAMPLE_CLEAN)
waveform_noise, sr2 = torchaudio.load(SAMPLE_NOISE)
assert sr == sr2 == SAMPLE_RATE
# The mixture waveform is a combination of clean and noise waveforms with a desired SNR.
target_snr = 3
waveform_mix = generate_mixture(waveform_clean, waveform_noise, target_snr)

Note: To improve computational robustness, it is recommended to represent the waveforms as double-precision floating point (torch.float64 or torch.double) values.

3.2. Compute STFT coefficients

N_FFT = 1024
N_HOP = 256
stft = torchaudio.transforms.Spectrogram(
istft = torchaudio.transforms.InverseSpectrogram(n_fft=N_FFT, hop_length=N_HOP)

stft_mix = stft(waveform_mix)
stft_clean = stft(waveform_clean)
stft_noise = stft(waveform_noise)

3.2.1. Visualize mixture speech

We evaluate the quality of the mixture speech or the enhanced speech using the following three metrics:

  • signal-to-distortion ratio (SDR)

  • scale-invariant signal-to-noise ratio (Si-SNR, or Si-SDR in some papers)

  • Perceptual Evaluation of Speech Quality (PESQ)

We also evaluate the intelligibility of the speech with the Short-Time Objective Intelligibility (STOI) metric.

plot_spectrogram(stft_mix[0], "Spectrogram of Mixture Speech (dB)")
evaluate(waveform_mix[0:1], waveform_clean[0:1])
Audio(waveform_mix[0], rate=SAMPLE_RATE)
Spectrogram of Mixture Speech (dB)
SDR score: 4.140362181778027
Si-SNR score: 4.104058905536078
PESQ score: 2.0084526538848877
STOI score: 0.7724339398714715

3.2.2. Visualize clean speech

plot_spectrogram(stft_clean[0], "Spectrogram of Clean Speech (dB)")
Audio(waveform_clean[0], rate=SAMPLE_RATE)
Spectrogram of Clean Speech (dB)

3.2.3. Visualize noise

plot_spectrogram(stft_noise[0], "Spectrogram of Noise (dB)")
Audio(waveform_noise[0], rate=SAMPLE_RATE)
Spectrogram of Noise (dB)

3.3. Define the reference microphone

We choose the first microphone in the array as the reference channel for demonstration. The selection of the reference channel may depend on the design of the microphone array.

You can also apply an end-to-end neural network which estimates both the reference channel and the PSD matrices, then obtains the enhanced STFT coefficients by the MVDR module.

3.4. Compute IRMs

def get_irms(stft_clean, stft_noise):
    mag_clean = stft_clean.abs() ** 2
    mag_noise = stft_noise.abs() ** 2
    irm_speech = mag_clean / (mag_clean + mag_noise)
    irm_noise = mag_noise / (mag_clean + mag_noise)
    return irm_speech[REFERENCE_CHANNEL], irm_noise[REFERENCE_CHANNEL]

irm_speech, irm_noise = get_irms(stft_clean, stft_noise)

3.4.1. Visualize IRM of target speech

plot_mask(irm_speech, "IRM of the Target Speech")
IRM of the Target Speech

3.4.2. Visualize IRM of noise

plot_mask(irm_noise, "IRM of the Noise")
IRM of the Noise

4. Compute PSD matrices

torchaudio.transforms.PSD() computes the time-invariant PSD matrix given the multi-channel complex-valued STFT coefficients of the mixture speech and the time-frequency mask.

The shape of the PSD matrix is (…, freq, channel, channel).

psd_transform = torchaudio.transforms.PSD()

psd_speech = psd_transform(stft_mix, irm_speech)
psd_noise = psd_transform(stft_mix, irm_noise)

5. Beamforming using SoudenMVDR

5.1. Apply beamforming

torchaudio.transforms.SoudenMVDR() takes the multi-channel complexed-valued STFT coefficients of the mixture speech, PSD matrices of target speech and noise, and the reference channel inputs.

The output is a single-channel complex-valued STFT coefficients of the enhanced speech. We can then obtain the enhanced waveform by passing this output to the torchaudio.transforms.InverseSpectrogram() module.

mvdr_transform = torchaudio.transforms.SoudenMVDR()
stft_souden = mvdr_transform(stft_mix, psd_speech, psd_noise, reference_channel=REFERENCE_CHANNEL)
waveform_souden = istft(stft_souden, length=waveform_mix.shape[-1])

5.2. Result for SoudenMVDR

plot_spectrogram(stft_souden, "Enhanced Spectrogram by SoudenMVDR (dB)")
waveform_souden = waveform_souden.reshape(1, -1)
evaluate(waveform_souden, waveform_clean[0:1])
Audio(waveform_souden, rate=SAMPLE_RATE)
Enhanced Spectrogram by SoudenMVDR (dB)
SDR score: 17.946234447509003
Si-SNR score: 12.215202612269849
PESQ score: 3.3447437286376953
STOI score: 0.871286447916186

6. Beamforming using RTFMVDR

6.1. Compute RTF

TorchAudio offers two methods for computing the RTF matrix of a target speech:

6.2. Apply beamforming

torchaudio.transforms.RTFMVDR() takes the multi-channel complexed-valued STFT coefficients of the mixture speech, RTF matrix of target speech, PSD matrix of noise, and the reference channel inputs.

The output is a single-channel complex-valued STFT coefficients of the enhanced speech. We can then obtain the enhanced waveform by passing this output to the torchaudio.transforms.InverseSpectrogram() module.

mvdr_transform = torchaudio.transforms.RTFMVDR()

# compute the enhanced speech based on F.rtf_evd
stft_rtf_evd = mvdr_transform(stft_mix, rtf_evd, psd_noise, reference_channel=REFERENCE_CHANNEL)
waveform_rtf_evd = istft(stft_rtf_evd, length=waveform_mix.shape[-1])

# compute the enhanced speech based on F.rtf_power
stft_rtf_power = mvdr_transform(stft_mix, rtf_power, psd_noise, reference_channel=REFERENCE_CHANNEL)
waveform_rtf_power = istft(stft_rtf_power, length=waveform_mix.shape[-1])

6.3. Result for RTFMVDR with rtf_evd

plot_spectrogram(stft_rtf_evd, "Enhanced Spectrogram by RTFMVDR and F.rtf_evd (dB)")
waveform_rtf_evd = waveform_rtf_evd.reshape(1, -1)
evaluate(waveform_rtf_evd, waveform_clean[0:1])
Audio(waveform_rtf_evd, rate=SAMPLE_RATE)
Enhanced Spectrogram by RTFMVDR and F.rtf_evd (dB)
SDR score: 11.880210635282511
Si-SNR score: 10.714419996130093
PESQ score: 3.083890914916992
STOI score: 0.8261544910053269

6.4. Result for RTFMVDR with rtf_power

plot_spectrogram(stft_rtf_power, "Enhanced Spectrogram by RTFMVDR and F.rtf_power (dB)")
waveform_rtf_power = waveform_rtf_power.reshape(1, -1)
evaluate(waveform_rtf_power, waveform_clean[0:1])
Audio(waveform_rtf_power, rate=SAMPLE_RATE)
Enhanced Spectrogram by RTFMVDR and F.rtf_power (dB)
SDR score: 15.42459027693453
Si-SNR score: 13.035440892134858
PESQ score: 3.487997531890869
STOI score: 0.8798278461896283