  We study the problem of recovering the underlining sparse signals from clean
or noisy phaseless measurements. Due to the sparse prior of signals, we adopt
an L0regularized variational model to ensure only a small number of nonzero
elements being recovered in the signal and two different formulations are
established in the modeling based on the choices of data fidelity, i.e., L2and
L1norms. We also propose efficient algorithms based on the Alternating
Direction Method of Multipliers (ADMM) with convergence guarantee and nearly
optimal computational complexity. Thanks to the existence of closed-form
solutions to all subproblems, the proposed algorithm is very efficient with low
computational cost in each iteration. Numerous experiments show that our
proposed methods can recover sparse signals from phaseless measurements with
higher successful recovery rates and lower computation cost compared with the
state-of-art methods.
