Speech super-resolution (SSR) aims to recover a high resolution (HR) speech
from its corresponding low resolution (LR) counterpart. Recent SSR methods
focus more on the reconstruction of the magnitude spectrogram, ignoring the
importance of phase reconstruction, thereby limiting the recovery quality. To
address this issue, we propose mdctGAN, a novel SSR framework based on modified
discrete cosine transform (MDCT). By adversarial learning in the MDCT domain,
our method reconstructs HR speeches in a phase-aware manner without vocoders or
additional post-processing. Furthermore, by learning frequency consistent
features with self-attentive mechanism, mdctGAN guarantees a high quality
speech reconstruction. For VCTK corpus dataset, the experiment results show
that our model produces natural auditory quality with high MOS and PESQ scores.
It also achieves the state-of-the-art log-spectral-distance (LSD) performance
on 48 kHz target resolution from various input rates. Code is available from
this https URL

提出基于 MDCT 的 mdctGAN SSR 框架，通过敌对学习在 MDCT 域中以相位感知的方式重构高质量的语音，无需使用语音编解码器或其他额外的后处理，实验结果显示该模型在各种输入速率下，实现了 48 kHz 目标分辨率下的最新的对数组距离（LSD）性能。

使用修改的 DCT 频谱驯服基于 Transformer 的 GAN 进行语音超分辨率

mdctGAN: Taming transformer-based GAN for speech super-resolution with  Modified DCT spectra

Modern neural speech enhancement models usually include various forms of
phase information in their training loss terms, either explicitly or
implicitly. However, these loss terms are typically designed to reduce the
distortion of phase spectrum values at specific frequencies, which ensures they
do not significantly affect the quality of the enhanced speech. In this paper,
we propose an effective phase reconstruction strategy for neural speech
enhancement that can operate in noisy environments. Specifically, we introduce
a phase continuity loss that considers relative phase variations across the
time and frequency axes. By including this phase continuity loss in a
state-of-the-art neural speech enhancement system trained with reconstruction
loss and a number of magnitude spectral losses, we show that our proposed
method further improves the quality of enhanced speech signals over the
baseline, especially when training is done jointly with a magnitude spectrum
loss.

本文提出了一种有效的相位重建策略，可以在嘈杂的环境中操作，通过将相位连续性损失考虑在最先进的神经语音增强系统中，本文证明了我们所提出的方法在训练过程中，可以显著提高增强语音信号的质量。

相位连续性：学习语音增强的相位频谱导数

Phase Continuity: Learning Derivatives of Phase Spectrum for Speech Enhancement

This study investigates phase reconstruction for deep learning based monaural
talker-independent speaker separation in the short-time Fourier transform
(STFT) domain. The key observation is that, for a mixture of two sources, with
their magnitudes accurately estimated and under a geometric constraint, the
absolute phase difference between each source and the mixture can be uniquely
determined; in addition, the source phases at each time-frequency (T-F) unit
can be narrowed down to only two candidates. To pick the right candidate, we
propose three algorithms based on iterative phase reconstruction, group delay
estimation, and phase-difference sign prediction. State-of-the-art results are
obtained on the publicly available wsj0-2mix and 3mix corpus.

该研究采用深度学习对短时傅里叶变换领域中的单声道讲话人无关音频分离进行了相位重构实验，提出了三个基于迭代相位重构、组群延迟估计和相位差符号预测的算法，对公开的 wsj0-2mix 和 3mix 语料库进行了最先进的测试。