Skip to content

Instantly share code, notes, and snippets.

@tam17aki
Last active January 23, 2025 03:49
Show Gist options
  • Save tam17aki/23a700353260ae5be63b764218d6e481 to your computer and use it in GitHub Desktop.
Save tam17aki/23a700353260ae5be63b764218d6e481 to your computer and use it in GitHub Desktop.
An implementation of "Mel-Spectrogram Inversion via Alternating Direction Method of Multipliers" in Python.
# -*- coding: utf-8 -*-
"""Demonstration script for Mel-Spectrogram Inversion via ADMM.
Copyright (C) 2025 by Akira TAMAMORI
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
"""
import argparse
from typing import NamedTuple
import librosa
import numpy as np
import numpy.typing as npt
import soundfile as sf
from librosa.core.spectrum import istft, stft
from librosa.feature.spectral import melspectrogram
from pesq import pesq
from pystoi.stoi import stoi
from tqdm.auto import tqdm
class Arguments(NamedTuple):
"""Defines a class for miscellaneous configurations."""
in_file: str # input wav file
out_file: str # output (reconstructed) wav file
class FeatureConfig(NamedTuple):
"""Defines a class for configurations of feature extraction."""
n_mels: int # Number of Mel bins
n_fft: int = 1024 # FFT points
hop_length: int = 256 # Hop length
window: str = "hann" # Window type
class ADMMConfig(NamedTuple):
"""Defines a class for ADMM configurations."""
n_steps: int # Number of optimization steps
lambd: float # ADMM parameter
rho: float # ADMM parameter
def parse_args() -> tuple[Arguments, FeatureConfig, ADMMConfig]:
"""Parse command line arguments.
Returns:
arguments (Arguments): Miscellaneous configurations.
feat_config (FeatureConfig): Configurations of feature extraction.
admm_config (ADMMConfig): Configurations of ADMM.
"""
parser = argparse.ArgumentParser(
description="Demonstration script of ADMM-based mel-spectrogram inversion"
)
parser.add_argument("--in_file", type=str, default="in.wav", help="Input wav file")
parser.add_argument(
"--out_file",
type=str,
default="out.wav",
help="output (reconstructed) wav file",
)
parser.add_argument("--n_mels", type=int, default="80", help="Number of Mel bins")
parser.add_argument(
"--n_steps", type=int, default="500", help="Number of optimization steps"
)
parser.add_argument("--lambd", type=float, default="5000", help="ADMM parameter")
parser.add_argument("--rho", type=float, default="0.1", help="ADMM parameter")
args = parser.parse_args()
arguments = Arguments(in_file=args.in_file, out_file=args.out_file)
feat_config = FeatureConfig(n_mels=args.n_mels)
admm_config = ADMMConfig(n_steps=args.n_steps, lambd=args.lambd, rho=args.rho)
return arguments, feat_config, admm_config
def prox_pos(x: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
"""Proximity operator for non-negative constraint.
Args:
x (npt.NDArray[np.float64]): Input array.
Returns:
npt.NDArray[np.float64]: Non-negative version of input array.
"""
return np.maximum(x, 0)
def update_x(
y: npt.NDArray[np.float64],
z: npt.NDArray[np.complex128],
v: npt.NDArray[np.complex128],
config: ADMMConfig,
) -> npt.NDArray[np.complex128]:
"""Update complex STFT coefficients using the proximity operator.
Args:
y (npt.NDArray[np.float64]): Magnitude of STFT (Y).
z (npt.NDArray[np.complex128]): Complex STFT coefficients (Z).
v (npt.NDArray[np.complex128]): Dual variable (V).
config (Config): Configurations of ADMM.
Returns:
x_new (npt.NDArray[np.complex128]): Updated complex STFT coefficients (X).
"""
rho = config.rho
psi = z + v
abs_psi = np.abs(psi)
abs_psi = np.where(abs_psi == 0, 1e-8, abs_psi)
x_new_ = (y + rho * abs_psi) / (1 + rho)
x_new: npt.NDArray[np.complex128] = x_new_ * psi / abs_psi
return x_new
def update_w(
inv_mat: npt.NDArray[np.float64],
etm: npt.NDArray[np.float64],
y: npt.NDArray[np.float64],
u: npt.NDArray[np.float64],
config: ADMMConfig,
) -> npt.NDArray[np.float64]:
"""Update full-band magnitude using the linear system solution.
Args:
inv_mat (npt.NDArray[np.float64]): Inverse matrix in the algorithm.
etm (npt.NDArray[np.float64]): Product of tranpose of E and M (E^T @ M).
y (npt.NDArray[np.float64]): Magnitude of STFT (Y).
u (npt.NDArray[np.float64]): Dual variable (U).
config (ADMMConfig): Configurations of ADMM.
Returns:
w_new (npt.NDArray[np.float64]): Updated full-band magnitude (W).
"""
rho = config.rho
lambd = config.lambd
w_new = inv_mat @ (lambd * etm + rho * (y + u))
return w_new
def update_z(
x: npt.NDArray[np.complex128],
v: npt.NDArray[np.complex128],
config: FeatureConfig,
) -> npt.NDArray[np.complex128]:
"""Update complex STFT coefficients by projecting onto the STFT domain.
Args:
x (npt.NDArray[np.complex128]): Complex STFT coefficients (X).
v (npt.NDArray[np.complex128]): Dual variable (V).
config (FeatureConfig): Configurations of feature extraction.
Returns:
z_new (npt.NDArray[np.complex128]): Updated complex STFT coefficients (Z).
"""
n_fft = config.n_fft
hop_length = config.hop_length
window = config.window
z_new = stft(
istft(x - v, hop_length=hop_length, window=window),
n_fft=n_fft,
hop_length=hop_length,
window=window,
)
return z_new
def update_y(
x: npt.NDArray[np.complex128],
w: npt.NDArray[np.float64],
u: npt.NDArray[np.float64],
config: ADMMConfig,
) -> npt.NDArray[np.float64]:
"""Update magnitude of STFT using proximity operator with non-negative constraint.
Args:
x (npt.NDArray[np.complex128]): Complex STFT coefficients (X).
w (npt.NDArray[np.float64]): Full-band magnitude (W).
u (npt.NDArray[np.float64]): Dual variable (U).
config (ADMMConfig): Configurations of ADMM.
Returns:
y_new (npt.NDArray[np.float64]): Updated magnitude of STFT (Y).
"""
rho = config.rho
y_new = prox_pos((np.abs(x) + rho * (w - u))) / (1 + rho)
return y_new
def initialize_stft_from_mel(
mel_spec: npt.NDArray[np.float64], sr: int, n_fft: int
) -> npt.NDArray[np.complex128]:
"""Initialize STFT coefficients from mel-spectrogram using librosa.mel_to_stft.
Args:
mel_spec (npt.NDArray[np.float64]): Mel-spectrogram.
sr (int): Sampling rate.
n_fft (int): FFT size.
Returns:
npt.NDArray[np.complex128]: Initialized complex STFT coefficients.
"""
stft_coeffs: npt.NDArray[np.complex128] = librosa.feature.inverse.mel_to_stft(
mel_spec, sr=sr, n_fft=n_fft, power=1.0
)
random_phase = np.random.uniform(-np.pi, np.pi, stft_coeffs.shape)
random_complex: npt.NDArray[np.complex128] = np.exp(1j * random_phase)
return np.abs(stft_coeffs) * random_complex
def admm_mel_inversion(
mel_spec: npt.NDArray[np.float64],
sr: int,
feat_config: FeatureConfig,
admm_config: ADMMConfig,
) -> npt.NDArray[np.float64]:
"""Perform ADMM-based mel-spectrogram inversion.
This function implements mel-spectrogram inversion using the Alternating Direction
Method of Multipliers (ADMM) algorithm, as described in the following paper:
"Mel-Spectrogram Inversion via Alternating Direction Method of Multipliers"
Yoshiki Masuyama, Natsuki Ueno, and Nobutaka Ono
arXiv:2501.05557, 2025
Args:
mel_spec (npt.NDArray[np.float64]): Mel spectrogram.
sr (int): Sampling rate.
feat_config (FeatureConfig): Configurations of feature extraction.
admm_config (ADMMConfig): Configurations of ADMM.
Returns:
npt.NDArray[np.float64]: Reconstructed time-domain signal.
"""
n_mels = mel_spec.shape[0]
mel_filt = librosa.filters.mel(sr=sr, n_fft=feat_config.n_fft, n_mels=n_mels)
x = initialize_stft_from_mel(mel_spec, sr, feat_config.n_fft)
z = x
v = np.zeros_like(x, dtype=np.complex128)
y = np.abs(x)
w = y
u = np.zeros_like(y)
ete = np.dot(mel_filt.T, mel_filt)
etm = np.dot(mel_filt.T, mel_spec)
inv_mat = np.linalg.inv(
admm_config.lambd * ete + admm_config.rho * np.eye(ete.shape[0])
)
for _ in tqdm(
range(admm_config.n_steps),
bar_format="{desc}: {percentage:3.0f}% ({n_fmt} of {total_fmt}) |{bar}|"
+ " Elapsed Time: {elapsed} ETA: {remaining} ",
ascii=" #",
):
x = update_x(y, z, v, admm_config)
w = update_w(inv_mat, etm, y, u, admm_config)
z = update_z(x, v, feat_config)
y = update_y(np.abs(x), w, u, admm_config)
v = v + z - x
u = u + y - w
return istft(x, hop_length=feat_config.hop_length, window=feat_config.window)
def calculate_estoi(
orig_signal: npt.NDArray[np.float64],
reconst_signal: npt.NDArray[np.float64],
sr: int,
) -> float:
"""Calculate Extended Short-Time Objective Intelligibility (ESTOI).
Args:
orig_signal (npt.NDArray[np.float64]): Original time-domain signal.
reconst_signal (npt.NDArray[np.float64]): Reconstructed time-domain signal.
sr (int): Sampling rate.
Returns:
float: ESTOI score.
"""
if orig_signal.size > reconst_signal.size:
orig_signal = orig_signal[: reconst_signal.size]
else:
reconst_signal = reconst_signal[: orig_signal.size]
estoi_score: float = stoi(orig_signal, reconst_signal, sr, extended=True)
return estoi_score
def calculate_pesq(
orig_signal: npt.NDArray[np.float64],
reconst_signal: npt.NDArray[np.float64],
sr: int,
) -> float:
"""Calculate Perceptual Evaluation of Speech Quality (PESQ).
Args:
orig_signal (npt.NDArray[np.float64]): Original time-domain signal.
reconst_signal (npt.NDArray[np.float64]): Reconstructed time-domain signal.
sr (int): Sampling rate.
Returns:
float: PESQ score.
"""
pesq_score: float = pesq(sr, orig_signal, reconst_signal, "wb")
return pesq_score
def calculate_scm(
orig_spec: npt.NDArray[np.float64],
reconst_spec: npt.NDArray[np.float64],
) -> float:
"""Calculate Spectral Convergence Measure (SCM).
Args:
orig_spec (npt.NDArray[np.float64]): Original mel-spectrogram.
reconst_spec (npt.NDArray[np.float64]): Reconstructed mel-spectrogram.
Returns:
scm_score (float): SCM value in dB.
"""
numerator = np.linalg.norm(np.abs(reconst_spec) - orig_spec)
denominator = np.linalg.norm(orig_spec)
if denominator == 0:
return -float("inf")
scm_score: float = 20 * np.log10(numerator / denominator)
return scm_score
def main() -> None:
"""Perform demonstration."""
args, feat_config, admm_config = parse_args()
orig_signal, sr = sf.read(args.in_file)
mel_spec = melspectrogram(
y=orig_signal,
sr=sr,
n_fft=feat_config.n_fft,
hop_length=feat_config.hop_length,
window=feat_config.window,
power=1.0,
)
reconst_signal = admm_mel_inversion(mel_spec, sr, feat_config, admm_config)
sf.write(args.out_file, reconst_signal, sr)
reconst_mel_spec = melspectrogram(
y=reconst_signal,
sr=sr,
n_fft=feat_config.n_fft,
hop_length=feat_config.hop_length,
window=feat_config.window,
power=1.0,
)
estoi_score = calculate_estoi(orig_signal, reconst_signal, sr)
pesq_score = calculate_pesq(orig_signal, reconst_signal, sr)
scm_score = calculate_scm(mel_spec, reconst_mel_spec)
print(
f"ESTOI = {estoi_score:.6f}, "
+ f"PESQ = {pesq_score:.6f}, "
+ f"SCM [dB] = {scm_score:.6f}"
)
if __name__ == "__main__":
main()
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment