Estimating a Signal from a Magnitude Spectrogram via Convex Optimization

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.