  The problem of recovering a signal from its Fourier magnitude is of paramount
importance in various fields of engineering and applied physics. Due to the
absence of Fourier phase information, some form of additional information is
required in order to be able to uniquely, efficiently and robustly identify the
underlying signal. Inspired by practical methods in optical imaging, we
consider the problem of signal reconstruction from the Short-Time Fourier
Transform (STFT) magnitude. We first develop conditions under which the STFT
magnitude is an almost surely unique signal representation. We then consider a
semidefinite relaxation-based algorithm (STliFT) and provide recovery
guarantees. Numerical simulations complement our theoretical analysis and
provide directions for future work.
