We develop two techniques based on alternating minimization and
alternating directions method of multipliers for phase retrieval (PR)
by employing a variable-splitting approach in a maximum likelihood
estimation framework. This leads to an additional equality constraint,
which is incorporated in the optimization framework using a
quadratic penalty. Both algorithms are iterative, wherein the updates
are computed in closed-form. Experimental results show that: (i)
the proposed techniques converge faster than the state-of-the-art PR
algorithms; (ii) the complexity is comparable to the state of the art;
and (iii) the performance does not depend critically on the choice
of the penalty parameter. We also show how sparsity can be incorporated
within the variable splitting framework and demonstrate
concrete applications to image reconstruction in frequency-domain
optical-coherence tomography.