Neural Network-Based Speech Reconstruction from Undersampled STFT Magnitude Data

We demonstrate that a simple neural network is able to reconstruct audio signals from half as many short-time Fourier transform magnitude measurements as the audio signals have dimensions. In this setting, the short-time Fourier transform is not invertible and classical methods for short-time Fourier transform phase retrieval fail. The neural network-based approach is efficient and continues to work in situations where more data is available. In particular, it outperforms Fast Griffin-Lim in a setting where real phase retrieval is theoretically impossible.