  Retrieving a signal from its triple correlation spectrum, also called
bispectrum, arises in a wide range of signal processing problems. Conventional
methods do not provide an accurate inversion of bispectrum to the underlying
signal. In this paper, we present an approach that uniquely recovers signals
with finite spectral support (band-limited signals) from at least $3B$
measurements of its bispectrum function (BF), where $B$ is the signal's
bandwidth. Our approach also extends to time-limited signals. We propose a
two-step trust region algorithm that minimizes a non-convex objective function.
First, we approximate the signal by a spectral algorithm and then refine the
attained initialization based on a sequence of gradient iterations. Numerical
experiments suggest that our proposed algorithm is able to estimate
band-/time-limited signals from its BF for both complete and undersampled
observations.
