## On DC based Methods for Phase Retrieval. (arXiv:1810.09061v1 [cs.IT])

In this paper, we develop a new computational approach which is based on
minimizing the difference of two convex functionals (DC) to solve a broader
class of phase retrieval problems. The approach splits a standard nonlinear
least squares minimizing function associated with the phase retrieval problem
into the difference of two convex functions and then solves a sequence of
convex minimization sub-problems. For each subproblem, the Nesterov's
accelerated gradient descent algorithm or the Barzilai-Borwein (BB) algorithm
is used. In the setting of sparse phase retrieval, a standard $\ell_1$ norm
term is added into the minimization mentioned above. The subproblem is
approximated by a proximal gradient method which is solved by the
shrinkage-threshold technique directly without iterations. In addition, a
modified Attouch-Peypouquet technique is used to accelerate the iterative
computation. These lead to more effective algorithms than the Wirtinger flow
(WF) algorithm and the Gauss-Newton (查看全文