  We consider the classical 1D phase retrieval problem. In order to overcome
the difficulties associated with phase retrieval from measurements of the
Fourier magnitude, we treat recovery from the magnitude of the short-time
Fourier transform (STFT). We first show that the redundancy offered by the STFT
enables unique recovery for arbitrary nonvanishing inputs, under mild
conditions. An efficient algorithm for recovery of a sparse input from the STFT
magnitude is then suggested, based on an adaptation of the recently proposed
GESPAR algorithm. We demonstrate through simulations that using the STFT leads
to improved performance over recovery from the oversampled Fourier magnitude
with the same number of measurements.
