mvdr_tutorial.py

"""
Speech Enhancement with MVDR Beamforming
========================================

**Author** `Zhaoheng Ni <zni@fb.com>`__

"""


######################################################################
# 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 :py:func:`torchaudio.transforms.PSD`.
# -  Estimate enhanced speech using MVDR modules
#    (:py:func:`torchaudio.transforms.SoudenMVDR` and
#    :py:func:`torchaudio.transforms.RTFMVDR`).
# -  Benchmark the two methods
#    (:py:func:`torchaudio.functional.rtf_evd` and
#    :py:func:`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__)


######################################################################
# 2. Preparation
# --------------
#
# First, we import the necessary packages and retrieve the data.
#
# The multi-channel audio example is selected from
# `ConferencingSpeech <https://github.com/ConferencingSpeech/ConferencingSpeech2021>`__
# 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 <https://www.openslr.org/93/>`__ (Apache License
#    v.2.0)
# -  ``noise-sound-bible-0038.wav`` from
#    `MUSAN <http://www.openslr.org/17/>`__ (Attribution 4.0
#    International — CC BY 4.0)
#

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

SAMPLE_RATE = 16000
SAMPLE_CLEAN = download_asset("tutorial-assets/mvdr/clean_speech.wav")
SAMPLE_NOISE = download_asset("tutorial-assets/mvdr/noise.wav")


######################################################################
# 2.1. 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()


######################################################################
# 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
waveform_mix = waveform_clean + waveform_noise


######################################################################
# 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
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#

plot_spectrogram(stft_mix[0], "Spectrogram of Mixture Speech (dB)")
Audio(waveform_mix[0], rate=SAMPLE_RATE)


######################################################################
# 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
# -----------------------
#
# :py:func:`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
# ~~~~~~~~~~~~~~~~~~~~~~
#
# :py:func:`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
# :py:func:`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)
print(f"Si-SNR score: {si_snr(waveform_souden, waveform_clean[0:1])}")
Audio(waveform_souden, rate=SAMPLE_RATE)


######################################################################
# 6. Beamforming using RTFMVDR
# ----------------------------
#


######################################################################
# 6.1. Compute RTF
# ~~~~~~~~~~~~~~~~
#
# TorchAudio offers two methods for computing the RTF matrix of a
# target speech:
#
# -  :py:func:`torchaudio.functional.rtf_evd`, which applies eigenvalue
#    decomposition to the PSD matrix of target speech to get the RTF matrix.
#
# -  :py:func:`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
# ~~~~~~~~~~~~~~~~~~~~~~
#
# :py:func:`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
# :py:func:`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)
print(f"Si-SNR score: {si_snr(waveform_rtf_evd, waveform_clean[0:1])}")
Audio(waveform_rtf_evd, rate=SAMPLE_RATE)


######################################################################
# 6.4. Result for RTFMVDR with `rtf_power`
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#

plot_spectrogram(stft_rtf_power, "Enhanced Spectrogram by RTFMVDR and F.rtf_evd (dB)")
waveform_rtf_power = waveform_rtf_power.reshape(1, -1)
print(f"Si-SNR score: {si_snr(waveform_rtf_power, waveform_clean[0:1])}")
Audio(waveform_rtf_power, rate=SAMPLE_RATE)