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An implementation of "Griffin-Lim Like Phase Recovery via Alternating Direction Method of Multipliers" in Python.
# -*- coding: utf-8 -*-
"""Demonstration script for Griffin-Lim like phase recovery 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 numpy as np
import numpy.typing as npt
import soundfile as sf
from librosa.core.spectrum import istft, stft
from pesq import pesq
from pystoi.stoi import stoi
class Arguments(NamedTuple):
"""Defines a class for miscellaneous configurations."""
in_file: str # input wav file
out_file: str # output (reconstructed) wav file
class ADMMConfig(NamedTuple):
"""Defines a class for ADMM configurations."""
rho: float # ADMM parameter
n_steps: int # Number of optimization steps
class FeatureConfig(NamedTuple):
"""Defines a class for configurations of feature extraction."""
n_fft: int = 1024 # FFT points
hop_length: int = 256 # Hop length
window: str = "hann" # Window type
def check_positive_float(value: str) -> float:
"""Check positivity of float value.
Args:
value (str): Float value in string.
Returns:
fvalue (float): Positive float value.
Raises:
ArgumentTypeError: An error occurred in taking non-positive float value.
"""
fvalue: float = -1.0
try:
fvalue = float(value)
except ValueError as exc:
raise argparse.ArgumentTypeError(f"'{value}' is invalid float value.") from exc
if fvalue <= 0:
raise argparse.ArgumentTypeError(f"{value} is an invalid positive float value")
return fvalue
def check_positive_int(value: str) -> int:
"""Check positivity of integer value.
Args:
value (str): Integer value in string.
Returns:
ivalue (int): Positive integer value.
Raises:
ArgumentTypeError: An error occurred in taking non-positive integer value.
"""
ivalue: int = -1
try:
ivalue = int(value)
except ValueError as exc:
raise argparse.ArgumentTypeError(f"'{value}' is invalid int value.") from exc
if ivalue <= 0:
raise argparse.ArgumentTypeError(f"{value} is an invalid positive int value.")
return ivalue
def parse_args() -> tuple[Arguments, ADMMConfig]:
"""Parse command line arguments.
Returns:
arguments (Arguments): Miscellaneous configurations.
admm_config (ADMMConfig): Configurations of ADMM.
"""
parser = argparse.ArgumentParser(
description="Demonstration script for Griffin-Lim like phase recovery via ADMM"
)
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 wav file"
)
parser.add_argument(
"--rho", type=check_positive_float, default="0.1", help="ADMM parameter"
)
parser.add_argument(
"--n_steps",
type=check_positive_int,
default="500",
help="Number of optimization steps",
)
args = parser.parse_args()
arguments = Arguments(in_file=args.in_file, out_file=args.out_file)
admm_config = ADMMConfig(rho=args.rho, n_steps=args.n_steps)
return arguments, admm_config
def amp_constrained_proj(
x: npt.NDArray[np.complex128], amp_spec: npt.NDArray[np.float64]
) -> npt.NDArray[np.complex128]:
"""Perform amplitude-constrained projection.
This projection operation replaces the magnitude of each element in
the input complex spectrogram `x` with the corresponding value in the
target amplitude spectrogram `amp_spec`, while preserving the phase
spectrogram from the input `x`
Args:
x (npt.NDArray[np.complex128]): complex-valued spectrogram.
amp_spec (npt.NDArray[np.float64]): amplitude spectrogram.
Returns:
projected (npt.NDArray[np.complex128]): projected complex-valued spectrogram.
"""
y = amp_spec * np.exp(1j * np.angle(x))
projected: npt.NDArray[np.complex128] = y.astype(np.complex128)
return projected
def consistency_proj(
x: npt.NDArray[np.complex128], n_fft: int, hop_length: int, window: str
) -> npt.NDArray[np.complex128]:
"""Perform linear projection satifying STFT consistency criterion.
Args:
x (npt.NDArray[np.complex128]): complex-valued spectrogram.
n_fft (int): FFT window size.
hop_length (int): Hop length.
window (str): Window type.
Returns:
projected (npt.NDArray[np.complex128]): projected spectrogram.
"""
projected = stft(
istft(x, hop_length=hop_length, window=window),
n_fft=n_fft,
hop_length=hop_length,
window=window,
)
return projected
def proximity_squared(
x: npt.NDArray[np.complex128], rho: float, n_fft: int, hop_length: int, window: str
) -> npt.NDArray[np.complex128]:
"""Apply proximity operator of the squared distance to complex-valued spectrogram.
Args:
x (npt.NDArray[np.complex128]): complex-valued spectrogram.
rho (float): ADMM parameter.
n_fft (int): FFT window size.
hop_length (int): Hop length.
window (str): Window type.
Returns:
npt.NDArray[np.complex128]: mixture of input and its projected spectrogram.
"""
return (rho * x + consistency_proj(x, n_fft, hop_length, window)) / (1.0 + rho)
def admm_phase_recovery(
amp_spec: npt.NDArray[np.float64],
feat_config: FeatureConfig,
admm_config: ADMMConfig,
) -> npt.NDArray[np.complex128]:
"""Perform ADMM-based phase recovery.
This function implements phase recovery using the Alternating Direction
Method of Multipliers (ADMM) algorithm, as described in the following paper:
"Griffin-Lim like phase recovery via alternating direction method of multipliers,"
Yoshiki Masuyama, Kohei Yatabe, and Yasuhiro Oikawa
IEEE Signal Processing Letters, vol.26, no.1, pp.184--188, Jan. 2019.
https://ieeexplore.ieee.org/document/8552369
Args:
amp_spec (npt.NDArray[np.float64]): Amplitude spectrogram.
feat_config (FeatureConfig): Configurations of feature extraction.
admm_config (ADMMConfig): Configurations of ADMM.
Returns:
recovered_spec (npt.NDArray[np.complex128]): Recovered STFT spectrogram.
"""
n_fft = feat_config.n_fft
hop_length = feat_config.hop_length
window = feat_config.window
rho = admm_config.rho
n_steps = admm_config.n_steps
random_phase = np.random.uniform(-np.pi, np.pi, amp_spec.shape)
x = amp_spec * np.exp(1j * random_phase).astype(np.complex128)
z = x
u = np.zeros(amp_spec.shape, dtype=np.complex128)
for _ in range(n_steps):
x = amp_constrained_proj(z - u, amp_spec)
z = proximity_squared(x + u, rho, n_fft, hop_length, window)
u = u + x - z
recovered_spec: npt.NDArray[np.complex128] = x
return recovered_spec
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 main() -> None:
"""Perform demonstration."""
args, admm_config = parse_args()
feat_config = FeatureConfig()
n_fft = feat_config.n_fft
hop_length = feat_config.hop_length
window = feat_config.window
orig_signal, sr = sf.read(args.in_file)
amp_spec = np.abs(
stft(orig_signal, n_fft=n_fft, hop_length=hop_length, window=window)
)
recovered_spec = admm_phase_recovery(amp_spec, feat_config, admm_config)
reconst_signal = istft(recovered_spec, hop_length=hop_length, window=window)
sf.write(args.out_file, reconst_signal, sr)
estoi_score = calculate_estoi(orig_signal, reconst_signal, sr)
pesq_score = calculate_pesq(orig_signal, reconst_signal, sr)
print(f"ESTOI = {estoi_score:.6f}, PESQ = {pesq_score:.6f}")
if __name__ == "__main__":
main()
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