  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 that 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 discuss practical implementation details, including how the
method can be scaled up to larger examples.
