Estimating a Signal from a Magnitude Spectrogram via Convex Optimization
Abstract
The problem of recovering a signal from the magnitude of its short-time Fourier transform (STFT) is a longstanding one in audio signal processing. Existing approaches rely on heuristics which often perform poorly because of the nonconvexity of the problem. We introduce a formulation of the problem that lends itself to a tractable convex program. We observe that our method yields better reconstructions than the standard Griffin-Lim algorithm. We provide an algorithm and practical implementation details, including a discussion of how the method can be scaled up to larger examples.
中文速览
从音频信号的短时傅里叶变换（STFT）幅度谱中还原原始信号，是音频处理领域数十年来悬而未决的难题，核心障碍在于相位信息的缺失使得重建问题高度非凸、极易陷入局部最优。本文提出了一种名为 STliFT 的新方法，将原本对信号向量的估计"提升"为对一个矩阵的估计，从而把非凸问题转化为可高效求解的半正定规划（SDP）凸优化问题。实验表明，在从真实幅度谱恢复信号的任务中，STliFT 的成功率显著高于沿用多年的 Griffin-Lim 算法，尤其在帧移较小的情形下优势明显。这项工作为相位恢复提供了首个凸化框架，有望为音源分离、时间尺度变换等音频应用中的信号重建带来更可靠的理论保障。
原文 arXiv:1209.2076;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1209.2076v1