Demonstration script for phase recovery via rational function approximation.

ratiofunc.py

# -*- coding: utf-8 -*-
"""Demonstration script for phase recovery via rational function approximation.

Copyright (C) 2024 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
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The above copyright notice and this permission notice shall be included in all
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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
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SOFTWARE.
"""

import math
from dataclasses import dataclass

import numpy as np
import soundfile as sf
import torch
from pesq import pesq
from pystoi import stoi
from scipy import signal
from torch import nn, optim


@dataclass(frozen=True)
class NetworkConfig:
    """Class for network config."""

    input_channels: int = 257
    hidden_channels: int = 64
    kernel_size: int = 3
    n_order: int = 10


@dataclass(frozen=True)
class FeatureConfig:
    """Class for config of feature extraction."""

    hop_length: int = 128
    n_fft: int = 512
    rate: int = 16000
    in_wavefile: str = "input.wav"


@dataclass(frozen=True)
class TrainingConfig:
    """Class for training config."""

    n_epochs: int = 5000
    lr: float = 0.001
    n_interval: int = 1000


class PhaseRecoveryNet(nn.Module):
    """Phase recovery via rational function approximation."""

    def __init__(self):
        """Initialize class."""
        super().__init__()
        cfg = NetworkConfig()
        self.conv1 = nn.Conv1d(
            cfg.input_channels,
            cfg.hidden_channels,
            cfg.kernel_size,
            padding=(cfg.kernel_size - 1) // 2,
        )
        self.conv2 = nn.Conv1d(
            cfg.hidden_channels,
            cfg.hidden_channels,
            cfg.kernel_size,
            padding=(cfg.kernel_size - 1) // 2,
        )
        self.norm1 = nn.InstanceNorm1d(cfg.hidden_channels)
        self.norm2 = nn.InstanceNorm1d(cfg.hidden_channels)
        self.fc = nn.Linear(cfg.hidden_channels, (2 * cfg.n_order) * cfg.input_channels)
        self.activation = nn.ReLU()

    def forward(self, inputs):
        """Forward propagation."""
        inputs = inputs - torch.mean(inputs, dim=-1, keepdim=True)
        hidden = self.norm1(self.conv1(inputs))
        hidden = self.activation(hidden)
        hidden = self.norm2(self.conv2(hidden))
        hidden = self.activation(hidden)
        coefficients = self.fc(hidden.transpose(1, 2))
        return coefficients


def compute_ratiofunc(coeffs, freqs):
    """Compute a rational function."""
    n_spec, n_coeffs = freqs.shape
    n_batch, n_frame, _ = coeffs.size()
    coeffs = torch.reshape(coeffs, (n_batch, n_frame, n_spec, 2 * n_coeffs))
    numer_coeffs = coeffs[:, :, :, :n_coeffs]
    den_coeffs = coeffs[:, :, :, n_coeffs:]
    numer_coeffs = numer_coeffs.transpose(1, 2)
    den_coeffs = den_coeffs.transpose(1, 2)
    freqs = freqs.unsqueeze(0).expand(n_batch, n_spec, n_coeffs)
    freqs = freqs.unsqueeze(2).expand(n_batch, n_spec, n_frame, n_coeffs)
    numerator = (numer_coeffs * freqs).sum(dim=-1)
    denominator = (den_coeffs * freqs).sum(dim=-1)
    phase_spectrum = torch.atan2(numerator, denominator)
    return phase_spectrum


def compensate_phase(phase, win_len, n_batch, n_frame):
    """Compensate uniform linear phases."""
    pi_tensor = torch.Tensor([math.pi]).cuda()
    k = torch.arange(0, win_len // 2 + 1).cuda()
    angle_freq = (2 * pi_tensor / win_len) * k * (win_len - 1) / 2
    angle_freq = angle_freq.unsqueeze(1).expand(len(k), n_frame)
    angle_freq = angle_freq.unsqueeze(0).expand(n_batch, len(k), n_frame)
    phase = phase + torch.angle(torch.exp(1j * angle_freq))
    return phase


def extract_log_amp_and_phase(cfg: FeatureConfig):
    """Extract log magnitude and phase spectra from audio files."""
    filepath = cfg.in_wavefile
    n_fft = cfg.n_fft
    hop_length = cfg.hop_length
    audio, rate = sf.read(filepath)
    stfft = signal.ShortTimeFFT(
        win=signal.windows.hann(n_fft), hop=hop_length, fs=rate, mfft=n_fft
    )
    stft_data = stfft.stft(audio)
    amplitude = np.abs(stft_data).astype(np.float32)
    phase = np.angle(stft_data).astype(np.float32)
    amplitude = torch.from_numpy(amplitude)
    phase = torch.from_numpy(phase)
    log_amplitude = torch.log(amplitude + 1e-8)
    return log_amplitude, phase


def make_power_freq(n_splits, n_order):
    """Compute powers of angular frequencies."""
    freq = torch.tensor(np.linspace(0, np.pi, n_splits)).float()
    power_freq = []
    for order in range(n_order):
        power_freq.append((freq) ** order)
    power_freq = torch.stack(power_freq, dim=1)
    return power_freq


def loss_func(criterion, log_amplitude, pred_phase, target_phase):
    """Compute loss function."""
    pred = torch.exp(log_amplitude + 1j * pred_phase)
    target = torch.exp(log_amplitude + 1j * target_phase)
    loss = criterion(pred.real, target.real) + criterion(pred.imag, target.imag)
    return loss


@torch.no_grad()
def recover_phase(log_amplitude, model, power_freq):
    """Reconstruct phase."""
    coefficients = model(log_amplitude)
    phase = compute_ratiofunc(coefficients, power_freq)
    phase = phase.to("cpu").detach().numpy().copy()
    phase = np.squeeze(phase)
    return phase


def generate_wave(
    log_amplitude, phase, feat_cfg: FeatureConfig, train_cfg: TrainingConfig
):
    """Generate waveform from reconstructed phase."""
    log_amplitude = log_amplitude.to("cpu").detach().numpy().copy()
    log_amplitude = np.squeeze(log_amplitude)
    predict = np.exp(log_amplitude + 1j * phase)
    stfft = signal.ShortTimeFFT(
        win=signal.windows.hann(feat_cfg.n_fft),
        hop=feat_cfg.hop_length,
        fs=feat_cfg.rate,
        mfft=feat_cfg.n_fft,
    )
    audio = stfft.istft(predict)
    sf.write(f"output_{train_cfg.n_epochs}.wav", audio, feat_cfg.rate)


def eval_scores(feat_cfg: FeatureConfig, train_cfg: TrainingConfig):
    """Compute objective scores; PESQ, STOI and LSC."""
    reference, rate = sf.read(feat_cfg.in_wavefile)
    audio, _ = sf.read(f"output_{train_cfg.n_epochs}.wav")
    if len(audio) > len(reference):
        audio = audio[: len(reference)]
    else:
        reference = reference[: len(audio)]
    stfft = signal.ShortTimeFFT(
        win=signal.windows.hann(feat_cfg.n_fft),
        hop=feat_cfg.hop_length,
        fs=feat_cfg.rate,
        mfft=feat_cfg.n_fft,
    )
    ref_spec = stfft.stft(reference).T
    eval_spec = stfft.stft(audio).T
    lsc = np.linalg.norm(np.abs(ref_spec) - np.abs(eval_spec))
    lsc = lsc / np.linalg.norm(np.abs(ref_spec))
    lsc = 20 * np.log10(lsc)
    print(
        pesq(rate, reference, audio, "wb"),
        stoi(reference, audio, rate, extended=True),
        lsc,
    )


def main():
    """Perform model training."""
    net_cfg = NetworkConfig()
    feat_cfg = FeatureConfig()
    train_cfg = TrainingConfig()

    # setup training modules
    model = PhaseRecoveryNet().cuda()
    criterion = nn.MSELoss()
    optimizer = optim.Adam(model.parameters(), lr=train_cfg.lr)

    # feature extraction
    log_amplitude, target_phase = extract_log_amp_and_phase(feat_cfg)
    power_freq = make_power_freq(log_amplitude.size(0), net_cfg.n_order).cuda()
    log_amplitude = log_amplitude.unsqueeze(0).cuda()
    target_phase = target_phase.unsqueeze(0).cuda()

    # training
    model.train()
    for epoch in range(train_cfg.n_epochs):
        epoch_loss = 0
        optimizer.zero_grad()
        coefficients = model(log_amplitude)
        pred_phase = compute_ratiofunc(coefficients, power_freq)
        loss = loss_func(criterion, log_amplitude, pred_phase, target_phase)
        loss.backward()
        optimizer.step()
        epoch_loss = loss.item()
        if (epoch + 1) % train_cfg.n_interval == 0:
            print(f"Epoch [{epoch+1}/{train_cfg.n_epochs}], Loss: {epoch_loss:.4f}")

    # inference
    model.eval()
    phase = recover_phase(log_amplitude, model, power_freq)
    generate_wave(log_amplitude, phase, feat_cfg, train_cfg)
    eval_scores(feat_cfg, train_cfg)


if __name__ == "__main__":
    main()