Note

Click here to download the full example code

Speech Enhancement with MVDR Beamforming¶

1. Overview¶

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

Steps:

Generate an ideal ratio mask (IRM) by dividing the clean/noise magnitude by the mixture magnitude.
Estimate power spectral density (PSD) matrices using torchaudio.transforms.PSD().
Estimate enhanced speech using MVDR modules (torchaudio.transforms.SoudenMVDR() and torchaudio.transforms.RTFMVDR()).
Benchmark the two methods (torchaudio.functional.rtf_evd() and torchaudio.functional.rtf_power()) for computing the relative transfer function (RTF) matrix of the reference microphone.

import torch
import torchaudio
import torchaudio.functional as F

print(torch.__version__)
print(torchaudio.__version__)

1.13.1
0.13.1

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

SSB07200001\#noise-sound-bible-0038\#7.86_6.16_3.00_3.14_4.84_134.5285_191.7899_0.4735\#15217\#25.16333303751458\#0.2101221178590021.wav

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_RATE = 16000
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, 38.9MB/s]

  0%|          | 0.00/1.95M [00:00<?, ?B/s]
100%|##########| 1.95M/1.95M [00:00<00:00, 62.9MB/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")
    figure.suptitle(title)
    plt.colorbar(img, ax=axis)
    plt.show()


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")
    figure.suptitle(title)
    plt.colorbar(img, ax=axis)
    plt.show()


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)
    (
        sdr,
        _,
        _,
        _,
    ) = 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.

waveform_mix = waveform_mix.to(torch.double)
waveform_clean = waveform_clean.to(torch.double)
waveform_noise = waveform_noise.to(torch.double)

3.2. Compute STFT coefficients¶

N_FFT = 1024
N_HOP = 256
stft = torchaudio.transforms.Spectrogram(
    n_fft=N_FFT,
    hop_length=N_HOP,
    power=None,
)
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)

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)

3.2.3. Visualize noise¶

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

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.

REFERENCE_CHANNEL = 0

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")

3.4.2. Visualize IRM of noise¶

plot_mask(irm_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)

SDR score: 17.946234441342177
Si-SNR score: 12.215202605414326
PESQ score: 3.3447487354278564
STOI score: 0.8712864460530876

6. Beamforming using RTFMVDR¶

6.1. Compute RTF¶

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

torchaudio.functional.rtf_evd(), which applies eigenvalue decomposition to the PSD matrix of target speech to get the RTF matrix.
torchaudio.functional.rtf_power(), which applies the power iteration method. You can specify the number of iterations with argument n_iter.

rtf_evd = F.rtf_evd(psd_speech)
rtf_power = F.rtf_power(psd_speech, psd_noise, reference_channel=REFERENCE_CHANNEL)

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.