Phasesplit: A Variable Splitting Framework for Phase Retrieval

Abstract

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.