  In this paper, we present a new algorithm, called MagnitudeCut, for
recovering a signal from the phase of its Fourier transform. We casted our
recovering problem into a new convex optimization problem, and then solved it
by the block coordinate descent algorithm and the interior point algorithm, in
which the iteration process consists of matrix vector product and inner
product. We used the new method for reconstruction of a set of signal/image.
The simulation results reveal that the proposed MagnitudeCut method can
reconstruct the original signal with fewer sampling number of the phase
information than that of the Greedy algorithm and iterative method under the
same reconstruction error. Moreover, our algorithm can also reconstruct the
symmetric image from its Fourier phase.
