  We focus on an alignment-free method to estimate the underlying signal from a
large number of noisy randomly shifted observations. Specifically, we estimate
the mean, power spectrum, and bispectrum of the signal from the observations.
Since bispectrum contains the phase information of the signal, reliable
algorithms for bispectrum inversion is useful in many applications. We propose
a new algorithm using spectral decomposition of the normalized bispectrum
matrix for this task. For clean signals, we show that the eigenvectors of the
normalized bispectrum matrix correspond to the true phases of the signal and
its shifted copies. In addition, the spectral method is robust to noise. It can
be used as a stable and efficient initialization technique for local non-convex
optimization for bispectrum inversion.
